JPH09138870A - Image processing apparatus and method - Google Patents

Abstract

(57) Abstract: An image processing apparatus and method capable of aligning a plurality of surface shapes without finding correspondence between geometrical features on the surface shapes of a three-dimensional object. To do. SOLUTION: A cutting plane is set in a spatial region where two surface shapes of a three-dimensional object overlap, a cross-sectional shape is created for each surface shape by the cutting plane, and corresponding points on the created cross-sectional shape are By searching from each cross-sectional shape and rotating and translating one of the two surface shapes so that the sum of squares of the distances between the corresponding points found is minimized. , Align the position.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an image processing apparatus and method, and more particularly to aligning the surface shape of a three-dimensional object.

[0002]

2. Description of the Related Art Conventionally, there has been a method of acquiring the surface shape of a three-dimensional object by taking a distance image with a distance measuring device.

Then, there is a method of manually aligning the surface shapes by using a device such as a mouse or a keyboard while wearing a projected image of a plurality of surface shapes obtained with respect to the same object viewed from an arbitrary line-of-sight direction. .

Further, geometrical features such as corresponding edges are searched for on a plurality of surface shapes obtained for the same object, and the conversion relationship of the coordinate system of each surface shape is calculated from their positional relationship. There was a method of aligning by this.

[0005]

However, according to the above-mentioned prior art, when it is difficult to visually find a portion having a similar shape on a plurality of surface shapes, it is impossible to perform the alignment accurately. There was a problem. For example, natural objects such as person statues are difficult to align using conventional techniques.

Further, the above-mentioned prior art has a problem that it is difficult to perform accurate alignment when it is difficult to find correspondence of geometric features. For example, natural objects such as person statues are difficult to align using conventional techniques.

[0007]

In order to solve the above problems, in an image processing apparatus according to the present invention, a setting means for setting a cutting plane in a spatial region where a plurality of surface shapes of a three-dimensional object overlap each other. , Creating means for creating a cross-sectional shape on each of the plurality of surface shapes by the cutting surface set by the setting means, and points corresponding to each of the plurality of cross-sectional shapes created by the creating means, Of the plurality of surface shapes, at least one of a plurality of surface shapes, a first calculating means for calculating a value of a function determined by a distance between the plurality of corresponding points searched by the searching means, Adjusting means for adjusting the position of one surface shape; second calculating means for calculating the adjustment amount by the adjusting means such that the value of the function calculated by the first calculating means is minimized; Based on the adjustment amount computed by the second computing means, provided with control means for controlling said adjusting means.

Further preferably, the adjusting means rotates at least one surface shape among the plurality of surface shapes.

Further preferably, the adjusting means moves at least one surface shape among the plurality of surface shapes.

Further preferably, the adjusting means translates at least one surface shape among the plurality of surface shapes.

Preferably, the adjusting means rotates and translates at least one surface shape of the plurality of surface shapes.

Also preferably, the plurality of surface shapes are
It was obtained by measuring from multiple different directions.

Further preferably, the first calculation means is
A value of a sum of squares of distances between the corresponding points searched by the searching means is calculated.

Also preferably, the setting means is an x-axis,
A plurality of cutting planes perpendicular to the y-axis and the z-axis are set.

Further preferably, the adjusting means adjusts the position of the at least one surface shape in each of the x coordinate, the y coordinate and the z coordinate.

Further preferably, the plurality of surface shapes are
Have a common coordinate system.

Further preferably, the plurality of surface shapes are
Each has its own coordinate system.

Further preferably, the adjusting means, when adjusting the position of the at least one surface shape, changes the value of a coordinate conversion matrix for converting the coordinates of the surface shape into the coordinates of another surface shape. To make that adjustment.

In order to solve the above problems, in the image processing method according to the present invention, a setting step of setting a cutting plane in a spatial region where a plurality of surface shapes of a three-dimensional object overlap, and the setting step. A cutting step of creating a cross-sectional shape for each of the plurality of surface shapes by the cutting surface set in
A search step of searching a point corresponding to each of the plurality of cross-sectional shapes created in the creating step from the respective cross-sectional shapes;
A first calculation step of calculating a value of a function determined by the distances between the corresponding points searched in the searching step; and an adjustment for adjusting the position of at least one surface shape of the plurality of surface shapes. Step, a second calculation step of calculating the adjustment amount in the adjustment step such that the value of the function calculated in the first calculation step is minimized, and a second calculation step calculated in the second calculation step. And a control step of controlling the adjustment in the adjusting step based on the adjustment amount.

Also preferably, in the adjusting step,
At least one surface shape is rotated among the plurality of surface shapes.

Further preferably, in the adjusting step,
At least one surface shape of the plurality of surface shapes is moved.

Further preferably, in the adjusting step,
At least one surface shape of the plurality of surface shapes is translated.

Preferably, in the adjusting step,
Rotating and translating at least one surface shape of the plurality of surface shapes.

Preferably, the plurality of surface shapes are
It was obtained by measuring from multiple different directions.

Further preferably, in the first calculating step, a value of a sum of squares of distances between the plurality of corresponding points searched in the searching step is calculated.

Further preferably, in the setting step,
A plurality of cutting planes perpendicular to the x-axis, the y-axis, and the z-axis are set.

Further preferably, in the adjusting step,
X-coordinate, y-coordinate, z of the at least one surface shape
Adjust the position at each of the coordinates.

Further, preferably, the plurality of surface shapes are
Have a common coordinate system.

Preferably, the plurality of surface shapes are
Each has its own coordinate system.

Further preferably, in the adjusting step,
In adjusting the position of the at least one surface feature,
The adjustment is performed by changing the value of the coordinate conversion matrix that converts the coordinates of the surface shape into the coordinates of another surface shape.

[0031]

BEST MODE FOR CARRYING OUT THE INVENTION

[Embodiment 1] In Embodiment 1, a method for aligning two surface shapes obtained by measuring a three-dimensional object from two different directions using a distance measuring device will be described. Hereinafter, the two surface shapes are referred to as surface shape A and surface shape B. It is assumed that the two surface shapes have been roughly aligned in advance by a method of the related art or the like.

In the method of the first embodiment, a set of corresponding points on two surface shapes is extracted. Then, the surface shape B is rotated and moved in parallel so that the sum of the squares of the distances between the corresponding points is minimized to perform the alignment. Here, the corresponding points are searched for on the cross-sectional shape obtained by cutting the surface shape by the plane set in the three-dimensional space. By this method, the space for searching the corresponding points is limited to the two-dimensional plane, so that it is possible to obtain the corresponding points using a simple method that does not require the extraction of geometrical features. However, since the corresponding points obtained in a set of cross-sectional shapes are on the same plane, 6 degrees of freedom of space to be determined for alignment (translation in each coordinate axis direction and rotation around each coordinate axis)
Of these, only 3 degrees of freedom can be determined. Also, the corresponding points obtained by limiting the search space are not always the same points on the target object. Therefore, accurate alignment cannot be achieved with only one set of cross-sectional shapes. Therefore,
By repeating the fine adjustment of the alignment while changing the direction of the cut surface, the lack of the degree of freedom is compensated and the accuracy of the alignment is gradually increased.

FIG. 1 shows a three-dimensional shape alignment apparatus according to the first embodiment.

In FIG. 1, 105 is a first storage device for storing the processing procedure, and 106 is a second storage device for storing the data to be processed and the processing result data.

Reference numeral 107 denotes a CP for executing processing according to the processing procedure stored in the first storage device 105.
U is a unit, 104 is an input / output unit for data with an external device, and 108 is a bus connecting these units.

In the first storage device 105, p
Reference numeral 1 is a program for performing alignment processing of a three-dimensional surface shape, r1 is a routine for fine adjustment of alignment in p1, and r2 is a routine for calculating a convergence rate in p1. Yes, r11 is a routine for setting a cutting plane in r1, r12 is a routine for creating a cross-sectional shape in r1, and r13 is searching for a corresponding point on the cross-sectional shape in r1. Routine, r14
Is a routine that rotates and translates the surface shape in r1.

In the second storage device 106, d
1 is the coordinate value data of each point on the surface shape A input for the processing, and d2 is the coordinate value data of each point on the surface shape B input for the processing and calculated as a result of the processing. Yes, d3 is the data of the sectional shape A calculated as a result of the processing, d4 is the data of the sectional shape B calculated as the result of the processing, and d5 is the distance between the corresponding points calculated as the result of the processing. D6 is the coordinate data of the corresponding points calculated as a result of the processing.

Further, 101 is an input device for inputting various data, 102 is a display device for displaying the data stored in the second storage device, and 103 is stored in the second storage device. The printing unit prints the created data.

Next, FIG. 2 shows the flow of the entire processing of the first embodiment. The flow of processing will be described below with reference to FIG.

First, in step S201, the data of the surface shape A and the data of the surface shape B are input from the input / output unit 104 with the external device. The surface shape data are all made up of the coordinate values of discrete point groups on the surface of the three-dimensional object which is the object of measurement. Hereinafter, such a point group is referred to as a sample point on the surface shape. Here, the coordinates of all sample points on the surface shape A and the surface shape B are represented as coordinate values in a common coordinate system. The surface shape data input in this step is stored in the areas d1 and d2 of the second storage device 106. Next, step S2
Fine-tune the alignment at 02. Step S202 will be described in detail later. Then, in step S203, the evaluation value "convergence rate" used in the next step S204 is calculated. The method of calculating the convergence rate in step S203 will also be described in detail later. In step S204, it is determined based on the value of the convergence rate whether or not to perform the fine adjustment process for alignment again. If the convergence rate is less than a certain threshold value T _h , the fine adjustment process for alignment is terminated, and step S20
Go to 5. On the other hand, if the convergence rate is greater than or equal to the threshold value, the process returns to step S202. Finally, in step S205, the surface shape data aligned by the above processing is output from the input / output unit 104 with the external device, and the processing ends.

Next, the fine adjustment of the alignment in step S202 of FIG. 2 will be described in detail with reference to the flowcharts of FIGS. In the fine adjustment processing of alignment, as shown in the flowchart of FIG. 3, fine adjustment of alignment by a cutting plane perpendicular to each coordinate axis of the Z axis, Y axis, and X axis is performed in step S30.
The steps S1, S302, and S303 are sequentially performed. Then, FIG. 4 shows a flow of a fine adjustment process of alignment regarding each coordinate axis.

First, in step S401, cutting planes C _{1 to} C _t perpendicular to the coordinate axes are set at a plurality of locations in the area where the two three-dimensional shapes overlap. In the first embodiment, t = 3. The method of setting the cut surface in step S401 will be described in detail later. In the next step S402,
A counter k for identifying the cut surface is initialized to 1.
In step S403, cross-sectional shapes _obtained by cutting the surface shape A and the surface shape B along the cutting plane C _k are created. Below, the cross-sectional shape created from the surface shape A will be called cross-sectional shape A, and the cross-sectional shape created from the surface shape B will be called cross-sectional shape B. The cross-sectional shape data created in this step is stored in the areas d3 and d4 of the second storage device 106. This step S403 will be described later in detail. Next, in step S404, corresponding points on the cross-sectional shape are searched. The data of the corresponding points obtained in this step is stored in the area d6 of the second storage device 106. This step S404 will also be described in detail later. Then, in step S405, the counter k is incremented.
Next, in step S406, the counter k is compared with the number t of cut surfaces, and if k> t, it is determined that the processing has been completed for all cut surfaces, and the process proceeds to step S407. k
If ≤t, it is determined that there is an unprocessed cut surface, and the process returns to step S403. In step S407, the surface shape B is rotated and translated so that the function determined by the distance between the corresponding points is minimized. This step S407
The details will also be described later.

Here, the cut surface setting process in step S401 will be described in detail. First, the symbol Φ is X
Alternatively, it represents Y or Z and is used to identify the coordinate axis. Also, the range of Φ coordinates of the sample points on the surface shape A and the surface shape B is

[0044]

[Outside 1] Is represented by. At this time, in the fine adjustment processing of the alignment by the cutting plane perpendicular to the Φ axis, the equation of the cutting plane is as follows.

[0045]

[Outside 2] Where the symbol φ is the Φ coordinate, max (a, b) is the smallest value of a and b, and min (a, b) is a and b.
Is a function that returns a non-maximum value. Moreover, lambda is a number that determines the position of each cut surface in the overlapping region of the surface shape, in the present embodiment respectively cut surface C _1, C ₂ and C ₃ 0.2,0.5,0. It was set to 8.

Next, the details of the method of creating the sectional shape in step S403 will be described. The cross-sectional shape is expressed as an intersection of the cut surface and the surface shape and a set of sides connecting them. FIG. 5 shows a conceptual diagram of this cross-sectional shape creation processing.

In FIG. 5, reference numeral 501 denotes a certain surface shape, 5
Reference numeral 02 is a cut surface, and 503 is a part of a distance image corresponding to the surface shape 501. The measurement points v ₁ , v ₂ , v ₃ and v ₄ that form the smallest grid on the distance image and the line segments v ₁ v ₂ , v ₂ v ₃ , v ₃ v ₄ , v ₄ connecting these points. Consider v ₁ and v ₂ v ₄ . Note that points v ₁ , v ₂ , v ₃ and v ₄
Points on the surface shape corresponding to are points V ₁ , V ₂ and V, respectively.
₃ and V ₄ . Here, line segments v ₁ v ₂ , v ₂ v ₃ , v ₃
v ₄ , v ₄ v ₁ and v ₂ v ₄ are called two-dimensional line elements, and the corresponding line segments V ₁ V ₂ , V ₂ V ₃ , V ₃ V ₄ and V ₂ V ₄ are three-dimensional line elements. I will call it. In the cross-section shape creation process,
The intersection of the three-dimensional line element and the cut surface is obtained, and is set as the intersection of the cut surface and the surface shape.

For example, in the case of FIG. 5, the three-dimensional line element V
₁ V ₂ , V ₂ V ₄ and V ₃ V ₄ intersect the cutting plane, and the points G ₁ , G ₂ and G _{3 on} the respective three-dimensional dotted line elements are extracted as the intersections of the cutting plane and the surface shape. It Next, of all line segments connecting the intersections of the cut surface and the surface shape, the line segment that is the contour line of the cross-sectional shape is obtained. For this purpose, first, a point (hereinafter referred to as a projection point) obtained by mapping the intersection of the cut surface and the surface shape on the distance image is obtained. Next, of the line segments connecting the projection points, a line segment that does not intersect with the two-dimensional line element at a position other than the projection point is obtained, and the line segment on the surface shape corresponding to this is used as the line segment that constitutes the contour line of the cross-sectional shape To do. For example, in FIG. 5, among the line segments connecting the projected points g ₁ , g ₂ and g ₃ of the intersection points G ₁ , G ₂ and G ₃ , the line segments g ₁ g ₂ and g ₂ g ₃ intersect the two-dimensional line element. Therefore, the line segments G ₁ G ₂ and G ₂ G ₃ are obtained as a part of the contour line of the cross-sectional shape. By performing the above operation on all the minimum grids on the distance image, the point cloud on the cross-sectional shape and the contour line of the cross-sectional shape can be obtained.

Next, the process of extracting corresponding points in the set of sectional shapes in step S404 will be described in detail with reference to FIG. First, in FIG. 6, for each side of the cross-sectional shape B, the bisector of that side is obtained. Here, the bisecting point on the i-th side is represented as a point P _i .
Then, through the point P _i, the i-th among the intersection of the perpendicular lines and the cross-sectional shape A to the side, point obtains the closest to the point P _i P _i
Corresponding point Q _i . As described above, in the method of the first embodiment, the corresponding points on the cross-sectional shape are obtained without extracting the geometrical feature.

Next, referring to the flowchart of FIG. 7, step S4
The processing of 07 will be described in detail. First, step S
At 701, the amount of rotation about the coordinate axis perpendicular to the cutting plane and the amount of movement on the coordinate plane parallel to the cutting plane are obtained from the positional relationship of the corresponding points. This step S701 will be described in detail later.

Next, the coordinates of each sample point on the surface shape B are changed based on the rotation amount and the parallel movement amount obtained in step S701. First, in step S702, a counter i for identifying sample points is initialized to 1. Next, in step S703, the coordinates of the i-th sample point on the surface shape B are converted, and the coordinate data is stored in the second storage device 1.
The data is accumulated in the area d2 of 06. This step S703 will also be described later in detail.

Next, in step S704, the counter i is incremented. Then, in step S705, if the counter i is equal to or less than the number N of sample points on the surface shape B, it is determined that there are sample points for which coordinate conversion has not been performed, the process returns to step S703, and if i> N, The rotation / parallel movement processing of the surface shape B is ended assuming that the coordinate conversion processing has been completed for all the sample points.

Here, the calculation processing of the rotation amount and the parallel movement amount in step S701 will be described in detail.

First, in the fine adjustment processing of the alignment by the cutting plane perpendicular to the X axis, the rotation amount around the X axis and the parallel movement amounts in the Y axis direction and the Z axis direction are obtained. In addition, in the fine adjustment processing of the alignment by the cut surface perpendicular to the Y axis, the rotation amount around the Y axis and the parallel movement amounts in the X axis direction and the Z axis direction are obtained. Further, in the fine adjustment processing of the alignment by the cut surface perpendicular to the Z axis, the rotation amount around the Z axis and the parallel movement amounts in the X axis direction and the Y axis direction are obtained. Now, by performing the corresponding point search process on the cut planes C _{1 to} C _t ,
A set of m corresponding points (P ₁ , Q ₁ ), (P ₂ , Q ₂ ), ...
., (P _m , Q _m ) is obtained. The point P ₁ by rotation and translation in a parallel coordinate plane to the cutting plane about the vertical coordinate axis in the cut surface, P _2, ···, point P _m, respectively _{P '1, P' 2,} ··· , P ′ _m ,
As added combined value E for all corresponding points the square of the distance of the point P _'i and the point Q _i is minimized, and determines a rotation amount and translation amount.

Here, the coordinates of the corresponding points are represented by two-dimensional coordinates, ignoring the coordinates in the direction perpendicular to the cut surface. For example, in the fine adjustment processing of the alignment by the cutting plane perpendicular to the X axis, the coordinates of the corresponding points are represented by the Y coordinate and the Z coordinate system. Now, _let the coordinates of the points P _i and Q _i be (u _i ,
v _i ) and (U _i , V _i ), and θ and (t _u , t _v ) are the amounts of rotation and parallel movement to be obtained. Furthermore, c _w = c
If os θ and s _w = sin θ, then c _w and s _w are respectively given by the following equations.

[0056]

[Outside 3] here,

[0057]

[Outside 4] It is. Further, t _u and t _v are given by the following equations.

[0058]

[Outside 5]

Next, the coordinate conversion processing of the sample points in step S703 will be described in detail. Surface shape B
The coordinates of the i-th sample point above before being updated are (x _i ^B , y
_i ^B , z _i ^B ), the updated coordinates (X _i ^B , Y _i ^B ,
Z _i ^B ) can be obtained from the following equation.

[0060]

[Outside 6] However, φ represents X or Y or Z as described above,
Matrix

[0061]

[Outside 7] Is used for fine adjustment of alignment by a cutting plane perpendicular to the φ axis. The matrices M _X , M _Y, and M _Z are represented by Formula 9, Formula 10, and Formula 11, respectively.

[0062]

[Outside 8]

Next, the method of calculating the convergence rate in step S203 will be described. Now, if the sum of the squares of the distances between the corresponding points extracted in the i-th fine adjustment process for alignment in step S202 is represented as D _i, it means that the fine adjustment process for the k-th alignment is performed. The convergence rate R _k is expressed by the following equation.

[0064]

[Outside 9] However, D ₀ is a sufficiently large number.

Finally, FIG. 8 shows an example of the application result of this embodiment. FIG. 8 shows a projected image of two surface shapes viewed from a certain viewing direction. In FIG. 8, (a)
Is a projected image before alignment, and (b) is a projected image after completion of alignment.

Needless to say, the above-described alignment can be performed by changing the surface shape of the object to be processed a plurality of times, even when the number of surface shapes is more than two.

[Second Embodiment] In the first embodiment, the two surface shapes have a common coordinate system, and the coordinates of each sample point of the surface shape B are updated each time a fine adjustment process for alignment is performed. . On the other hand, in the second embodiment, it is assumed that the two surface shapes each have their own coordinate system, and the coordinate conversion matrix for converting the coordinates of the surface shape B into the coordinates of the surface shape A is obtained. At this time, the coordinate conversion matrix is updated without updating the coordinates of each sample point of the surface shape B. Hereinafter, the coordinate system of the surface shape A is called a coordinate system A, and the coordinate system of the surface shape B is called a coordinate system B.

The overall flow of processing in the second embodiment is shown in FIG. Steps S901, S903 and S90
4 are steps S201 and S203 of the first embodiment, respectively.
And S204. Also, step S905
Then, the value of each element of the coordinate conversion matrix is output.

Further, in the process of step S902, the coordinate conversion matrix is sequentially corrected by the cutting plane perpendicular to each coordinate axis of the coordinate system A.

Next, FIG. 10 shows the flow of the fine adjustment processing for the alignment with respect to each coordinate axis. Step S10
01 and S1004 are step S401 of the first embodiment.
And S404, but all coordinates are coordinate system A
Is the value at. Further, steps S1002 and S10
05 and S1006 are the same as steps S402, S405 and S406 of the first embodiment, respectively. When creating the cross-sectional shape B in step_S1003,
From the inverse transformation of the coordinate transformation matrix and the equation of the cutting plane set in the coordinate system A, the equation of the cutting plane in the coordinate system B is obtained and the points on the cross-sectional shape are extracted. Since the coordinates of the points extracted here are represented by the coordinate system B, the coordinates are converted into the coordinates in the coordinate system A by the coordinate conversion matrix, and step S1004.
It is used in the search for corresponding points in.

Here, assuming that the coordinate conversion matrix before performing step S1007 is M _P , step S100
7, the fine adjustment matrix is obtained from the rotation amount and the parallel movement amount obtained by the same processing as step S701 of the first embodiment.

[0072]

[Outside 10] To obtain the coordinate transformation matrix

[0073]

[Outside 11] To update. However, the matrix

[0074]

[Outside 12] Is expressed by Equation 9, Equation 10, and Equation 11. The initial value of the coordinate conversion matrix is the unit matrix.

In the second embodiment, since it is not necessary to perform coordinate conversion for all the sample points on the surface shape B, the calculation time is reduced as compared with the first embodiment.

[Third Embodiment] First and Second Embodiments
Method consists of a set of discrete points on the surface of the object.
It can be applied not only to the surface shape of a three-dimensional object, but also to fine adjustment of alignment of a three-dimensional shape model such as a triangular patch model. In this case, the points on the cross-sectional shape are extracted as the intersections of the sides of the patch and the cut surface.

[0077]

As described in detail above, according to the present invention,
It is possible to align a plurality of surface shapes without finding correspondence between geometrical features on the surface shapes.

[Brief description of the drawings]

FIG. 1 is a block diagram of a three-dimensional shape alignment device according to a first embodiment.

FIG. 2 is an overall flowchart of a three-dimensional shape alignment method according to the first embodiment.

FIG. 3 is a flowchart of a fine adjustment process for alignment.

FIG. 4 is a flow chart of a fine adjustment process of alignment regarding each coordinate axis.

FIG. 5 is a conceptual diagram of cross-section shape creation processing.

FIG. 6 is a conceptual diagram of corresponding point search.

FIG. 7 is a flowchart of surface shape rotation / parallel movement processing.

FIG. 8 is a diagram showing an example of an application result of the first embodiment.

FIG. 9 is an overall flowchart of a three-dimensional shape alignment method according to the second embodiment.

FIG. 10 is a flowchart of a coordinate conversion matrix update process for each coordinate axis according to the second embodiment.

[Explanation of symbols]

105 First storage device for storing processing procedure 106 Second storage device for storing processing target data and processing result data 107 CPU 104 Input / output unit of data with external device 101 Input device 102 Display device 103 printing device 108 bus

Claims (24)

[Claims] 1. A cross-sectional shape is set for each of the plurality of surface shapes by a setting unit that sets a cutting surface in a spatial region where a plurality of surface shapes of a three-dimensional object overlap, and a cutting surface set by the setting unit. Between a creating means for creating, a searching means for searching for a point corresponding to each of the plurality of cross-sectional shapes created by the creating means from the respective cross-sectional shapes, and a plurality of corresponding points searched by the searching means First calculation means for calculating the value of the function determined by the distance, adjustment means for adjusting the position of at least one surface shape of the plurality of surface shapes, and calculation by the first calculation means A second calculation of the adjustment amount by the adjustment means so that the value of the function is minimized.
An image processing apparatus, comprising: a calculation unit of 1) and a control unit that controls the adjustment unit based on the adjustment amount calculated by the second calculation unit. 2. The image processing apparatus according to claim 1, wherein the adjusting unit rotates at least one surface shape of the plurality of surface shapes. 3. The image processing apparatus according to claim 1, wherein the adjusting unit moves at least one surface shape of the plurality of surface shapes. 4. The image processing apparatus according to claim 1, wherein the adjusting unit translates at least one surface shape of the plurality of surface shapes in parallel. 5. The image processing apparatus according to claim 1, wherein the adjusting unit rotates and translates at least one surface shape of the plurality of surface shapes. 6. The image processing apparatus according to claim 1, wherein the plurality of surface shapes are obtained by measuring from a plurality of different directions. 7. The image processing apparatus according to claim 1, wherein the first calculation means calculates a value of a sum of squares of distances between a plurality of corresponding points searched by the search means. . 8. The image processing apparatus according to claim 1, wherein the setting unit sets a plurality of cutting planes perpendicular to the x-axis, the y-axis, and the z-axis. 9. The image processing apparatus according to claim 1, wherein the adjusting unit adjusts the position of each of the at least one surface shape at each of the x coordinate, the y coordinate, and the z coordinate. 10. The image processing apparatus according to claim 1, wherein the plurality of surface shapes have a common coordinate system. 11. The image processing apparatus according to claim 1, wherein each of the plurality of surface shapes has its own coordinate system. 12. The adjusting means, when adjusting the position of the at least one surface shape, changes the value of a coordinate conversion matrix for converting the coordinates of the surface shape into the coordinates of another surface shape, The image processing apparatus according to claim 11, wherein the adjustment is performed. 13. A setting step of setting a cutting plane in a spatial region where a plurality of surface shapes of a three-dimensional object overlap, and a cross-sectional shape for each of the plurality of surface shapes by the cutting plane set in the setting step Between a creating step to create, a searching step of searching a point corresponding to each of the plurality of cross-sectional shapes created in the creating step from the respective cross-sectional shapes, and a plurality of corresponding points searched in the searching step. A first calculating step of calculating a value of a function determined by a distance; an adjusting step of adjusting the position of at least one surface shape of the plurality of surface shapes; and a calculating step of the first calculating step. A second calculation step for calculating the adjustment amount in the adjustment step such that the value of the function is minimized, and the adjustment in the adjustment step is controlled based on the adjustment amount calculated in the second calculation step. Control process An image processing method characterized by being provided. 14. The image processing method according to claim 13, wherein in the adjusting step, at least one surface shape among the plurality of surface shapes is rotated. 15. The image processing method according to claim 13, wherein in the adjusting step, at least one surface shape among the plurality of surface shapes is moved. 16. The image processing method according to claim 13, wherein in the adjusting step, at least one surface shape of the plurality of surface shapes is translated. 17. The image processing method according to claim 13, wherein in the adjusting step, at least one surface shape among the plurality of surface shapes is rotated and translated. 18. The image processing method according to claim 13, wherein the plurality of surface shapes are obtained by measuring from a plurality of different directions. 19. The image processing method according to claim 13, wherein in the first calculating step, a value of a sum of squares of distances between the plurality of corresponding points searched in the searching step is calculated. . 20. In the setting step, an x-axis, a y-axis,
14. The image processing method according to claim 13, wherein a plurality of cutting planes perpendicular to the z-axis are set. 21. The adjusting step adjusts the position of each of the at least one surface shape in each of the x coordinate, the y coordinate, and the z coordinate.
The image processing method described in the above. 22. The image processing method according to claim 13, wherein the plurality of surface shapes have a common coordinate system. 23. The image processing method according to claim 13, wherein each of the plurality of surface shapes has its own coordinate system. 24. In the adjusting step, when adjusting the position of the at least one surface shape, by changing the value of a coordinate conversion matrix for converting the coordinates of the surface shape into the coordinates of another surface shape, The image processing method according to claim 23, wherein the adjustment is performed.