JP2000172741A - Method for calibrating drawing image - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a calibration method which unnecessitate working in which three-dimensional coordinates values for all of correspondence points are found from a drawing and also enables calibration even to drawing where dimension is written. SOLUTION: A projected point where a point in the three-dimensional space of a device is projected onto the trihedral drawing of the device is defined as a mutual correspondence point, and a point on an image is associated with the coordinates of the point in the three-dimensional space based on distance information between the correspondence point and a correspondence point. An evaluation function in which the equivalence of coordinates values in the three-dimensional space calculated from the correspondence point and the distance between the correspondence points are defined as constraint conditions is defined, and a conversion coefficient which satisfies the constraint conditions to the evaluation function and also minimizes function value, i.e., the conversion coefficient of each drawing image is calculated by a second order differential value gradient method.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

[0001] 1. Field of the Invention [0002] The present invention relates to a three-dimensional simulation system using computer graphics, and more particularly to a method of calibrating a drawing image in three-dimensional modeling using a design drawing of a device.

[0002]

2. Description of the Related Art With the improvement of computer graphics processing performance, three-dimensional computer graphics (3D
Various three-dimensional simulation systems using CG) have begun to be applied to industry. In particular, an industrial system is a system that models a real device (creates a three-dimensional model) and realizes various simulation functions and status display functions as a three-dimensional application.

In such a three-dimensional system, since a three-dimensional model is indispensable, the three-dimensional model must be created. When creating a three-dimensional model, what is problematic is the number of steps required for creation.

For example, when a device model is created, it is easier to create a model by dividing the device to be modeled into a primitive shape such as a rectangular parallelepiped or a cylinder than by modeling it with a free-form surface or the like. However, acquiring the spatial information (vertex coordinates) of those primitives takes time.

[0005] As a method for easily extracting the spatial information of the primitive, a model creation method using a device design drawing or a device drawing (device outline drawing / three-view drawing) has been proposed. Recently, CAD drawings have been advanced, but they are still stored in paper form. Such a paper drawing is digitized (raster imaged), taken into a computer as a drawing image, and a three-dimensional model is created based on the drawing image (see FIG. 3). In this method, since primitives are applied to the underlying drawing, there is no need to input numerical values for the model, thereby simplifying model creation.

In order to extract primitive spatial information from a drawing image, coordinates (X, Y, Z) of a point in a three-dimensional space corresponding to the point (u, v) on the image must be obtained. No. That is, it is necessary to find a conversion function (X, Y, Z) = f (u, v) that associates the point (u, v) on the image with the coordinates (X, Y, Z) of the point in the three-dimensional space. is there. The process of obtaining this conversion function from information on points on the image is called calibration.

Actually, a point (u, v) on one drawing image
Cannot obtain the three coordinate values of the point (X, Y, Z) in the three-dimensional space corresponding to this, for example, (X, Y) from the front view, but (Y, Z) from the side view. ), But only two coordinate values are obtained from the top view, such as (Z, X).

Accordingly, the calibration of the drawing image is performed by changing the point (u, v) on the drawing image to the point (X,
It can be defined as identifying a conversion function (X, Y) = f (u, v) corresponding to two partial coordinate values (X, Y) of (Y, Z). By combining multiple drawing images (X,
(Y, Z) are calculated (see FIG. 4).

Hereinafter, unless otherwise specified, the drawing image is
The three views of the device, (X, Y, Z) represent the coordinates of a point in a three-dimensional space, (X, Y) etc. represent the two coordinate values of that point,
Let (u, v) represent the pixel coordinate value on the drawing of the point projected on the three-view drawing of the point in the three-dimensional space.

Usually, the above conversion function can be represented by the following linear combination formula (affine transformation).

[0011]

(Equation 1)

The calibration of the drawing image can be formulated by calculating the conversion coefficients (m ₀₀ , m ₀₁ , m ₀₂ , m ₁₀ , m ₁₁ , m ₁₂ ) of the equation (1). In the ideal drawing, both m ₀₁ and m ₁₀ in the equation (1) are 0, but (m
₀₁ and m ₁₀ is a rotational transformation element), to be not treat them as 0 since the image that may contain rotational transformation in the process of digitizing.

A general calibration method calculates this coupling coefficient using three-dimensional coordinate values as follows.

[0014] (1) drawing the image on the point (u _i, v _i) and the point of the three-dimensional in space corresponding thereto _{(X i, Y i, Z} i) obtaining a (i = 1 to n: n pieces Point). (X _i , Y _i ,
Z _i ) is set based on the dimensional information of the device described on the drawing.

(2) If the estimated value of the transformed coordinates according to the equation (1) of (u _i , v _i ) is (X _ei , Y _ei ), the following equation is established.

[0016]

(Equation 2)

[0017] (3) the mean square error E _X between the actual coordinates and the estimated coordinate values, the E _Y are defined as follows.

[0018]

(Equation 3)

[0019] (4) E _X, transform coefficient m _ij for minimizing the E _Y
Is determined by the following equation.

[0020]

(Equation 4)

[0021]

In the conventional drawing calibration method, since the points on the drawing and the coordinates of the points in the three-dimensional space are used, the accuracy of the obtained conversion coefficients is relatively high, and Because it is formulated as a solution of the equation, it has the feature that it can be obtained stably. However, there are the following problems.

The three-dimensional coordinate values have to be obtained manually from the dimensional information described on the drawing, so that the number of work steps is large.

In the case of equipment drawings, if the dimensional information is only partially entered, three-dimensional coordinate values required for calibration may not be obtained.

An object of the present invention is to provide a calibration method which eliminates the need to obtain three-dimensional coordinate values for all corresponding points from a drawing, and can perform calibration even on a drawing having no dimensions. It is in.

[0025]

According to the present invention, a plurality of corresponding points are set for a three-view drawing image, and a conversion coefficient is obtained based on distance information between the corresponding points instead of the three-dimensional coordinate values. The amount of work for obtaining three-dimensional coordinate values in calibration is reduced using information that is easily obtained from the drawing, such as the distance between points, and is characterized by the following method.

In performing calibration for obtaining a conversion coefficient of a conversion function for associating a point on a drawing image of a device with the coordinates of a point in a three-dimensional space, and creating a three-dimensional model of the device from the drawing image using the conversion function. In the calibration, a projection point in which a point in a three-dimensional space of the device is projected on a three-view drawing of the device is set as a corresponding point, and based on distance information between the corresponding point and the corresponding point, an image is displayed on an image. It is characterized in that a point is associated with the coordinates of the point in the three-dimensional space.

Also, an evaluation function is defined in which the equivalence of the coordinate values in the three-dimensional space obtained from the corresponding points and the distance between the corresponding points are defined as constraints, and the evaluation function is satisfied with the constraint. In addition, the conversion coefficient for minimizing the function value is obtained by an optimization technique.

Further, in the above-mentioned optimizing method, the conversion coefficient of each drawing image is obtained by a second-order differential value gradient method from an evaluation function for the equivalence of the corresponding points set in each drawing of the three views. And

Further, the optimization method uses the evaluation function for the equivalence obtained by setting the equal-magnification projection condition and the equiangular rotation condition of the two views at the corresponding points set in the two views, and The conversion coefficient of each drawing image is obtained by a differential value gradient method.

Further, the parameters in the second-order differential value gradient method are set to initial values for preventing convergence to a local minimum and erroneous parameter estimation due to the actual distance between corresponding points.

[0031]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS In the description of this embodiment, first, setting of corresponding points, which are basic operations in calibration, and a basic algorithm of a calibration method will be described. Then, an embodiment in which the basic algorithm is applied to the three views and the two views will be described.

(1) Setting of Corresponding Points The corresponding points referred to here are projection points at which points in a three-dimensional space are projected on a three-view drawing. Although the corresponding points have different pixel coordinate values on each image, the projection source has the same three-dimensional coordinate values (see FIG. 4).

For example, a point P ₁ (u ₁ , v ₁ ) on the front view, a point P ₂ (u ₂ , v ₂ ) on the side view, and a point P ₂ on the top view
₃ (u ₃ , v ₃ ) and the same point (X, Y,
If Z) is a projection point on each drawing, P ₁ ,
P ₂ and P ₃ correspond to each other.

When performing the calibration,
A plurality of such corresponding points are set on each drawing image.

(2) Basic Algorithm of Calibration Here, for convenience, a front view is a view in which a model object is projected on a plane parallel to the XY plane, a side view is a view in which a model object is projected on a plane parallel to the YZ plane, and a top view. The figure is defined as a figure projected on a plane parallel to the ZX plane (FIG. 4 shows only a front view and a side view).

[0036] In this case, a point on the diagram the front _{^{(u i 1, v i 1}} ) 3 -dimensional coordinates of the projected source from _{(X i, Y i, Z} i) of (X _i,
Y _i ) is represented by a point (u _i2 , _{vi 2} ) on the side view and the top view,
From (u _i3 , v _i3 ), (Y _i , Z _i ) and (Z _i , X _i ) can be obtained by the following conversion equations, respectively.

[0037]

(Equation 5)

In the above equations (2) to (4), the numbers attached to the conversion coefficients (m ₀₀ ^{1 and the} like) and the points (u _i ^{2 and the} like) on the image represent the type of each drawing. The figure is denoted by 1, the side view is denoted by 2, and the top view is denoted by 3. I indicates the i-th number of the corresponding point. Here, the 0-th corresponding point (u ₀ ¹ , v ₀ ¹ ), (u
_{When the} three-dimensional coordinates for ( ₀ ² , v ₀ ² ) and (u ₀ ³ , v ₀ ³ ) are set to the origin coordinates (0, 0, 0), the following equations are obtained from equations (2) to (4).

[0039]

(Equation 6)

The above equations (5) to (7) are replaced by equations (2) to
By substituting into (4), the following equations (8) to (10) are obtained.

[0041]

(Equation 7)

Hereinafter, u _i ¹ -u ₀ ¹ , v _i ¹ -v ₀ ¹ , u _i ² -u
^{_{0 2, v i 2 -v 0}} 2, u i 3 -u 0 3, v i 3 -v 0 3 respectively u
By represented by ^{_{i 1, v i 1, u}} i 2, v i 2, u i 3, v i 3,
The following equation (1) obtained by reducing the conversion coefficient from equations (8) to (10)
1) to (13) are targeted.

[0043]

(Equation 8)

[0044] If the transform coefficients are set correctly, X _i obtained by the formula X _i and equation obtained by (11) (13)
Are equal, and similarly, Y _i obtained from Expressions (12) and (11) and Z _i obtained from Expressions (13) and (12) become equal.

Conversely, estimating a conversion coefficient that makes each three-dimensional coordinate value equal is the basis of the calibration method of the present invention.

In the calibration method of the drawings according to the present invention, the equivalence of the three-dimensional coordinate values obtained from the equations (11) to (13) is evaluated by an evaluation function (defined by a quadratic equation convex downward: a specific function). Is described in the embodiment), and a conversion coefficient is obtained by minimizing the evaluation function by an optimization method.

In the equations (11) to (13), 12
12 × 1 matrix (transform coefficient matrix) in which transform coefficients are arranged
^{_{The, m = (m 00 1,}} ..., m 11 1, m 00 2, ..., m 11 2, m 00 3,
.., M ₁₁ ³ ) ^T where T represents transposition, the evaluation function E considering the equivalence of the three-dimensional coordinate values can be expressed as E (m).

However, since the evaluation function using only the equivalence of the three-dimensional coordinates does not include the element of the size of the three-dimensional space where the model exists, only the correspondence of each conversion coefficient is obtained. A conversion factor that takes the absolute size into account is not obtained.

Therefore, for the corresponding points set in each drawing,
A plurality of actual distances (actual dimensional distances, not pixel distances on the image) between the two points are designated, and the distances are added to the evaluation function as constraint conditions.

Drawing i (i = 1: front view, 2: side view,
3: top view) on a two corresponding points _{^{(u p i, v p i}} ) and (u _q ^i, v
_Assuming that the actual distance from _q ⁱ ) is L, the constraint condition f to be satisfied by the conversion coefficient is defined by Expression (14).

[0051]

(Equation 9)

From equation (14), since the constraint condition f is a function of the conversion coefficient, it can be expressed as f (m).

In order for the conversion coefficient to be estimated in consideration of the absolute size, at least one of the equations (1
It is necessary to set the constraint condition represented by 4). The set of these constraint conditions (the condition number is K) is re-written as F (=
(F ₁ , f ₂ ,..., F _k ) ^T ), F can also be represented as F (m) because F is also a function of m.

It is to be noted that the distance between all the corresponding points is not set, and an arbitrary number of distances may be set as long as the distance is one or more. Further, the greater the number of set distance information, the better the accuracy of estimating the conversion coefficient.

The basic algorithm of the calibration method shown in the drawing is summarized as follows.

(1) An evaluation function (a downwardly convex quadratic expression) is defined for the equivalence of the three-dimensional coordinate values obtained from the conversion coefficients and the corresponding point coordinates on the drawing.

(2) Distance information for a corresponding point set on the drawing is used as a constraint condition.

(3) A function obtained by combining the above (1) and (2) is defined as an overall evaluation function H.

(4) With respect to the evaluation function defined in (3), the evaluation function in (1) is minimized, and a conversion coefficient satisfying the constraint condition in (2) is obtained by an optimization method.

The mathematical expressions (1) to (4) are as follows.

(A) Evaluation function of equivalence of three-dimensional coordinate values =
E (m) (B) the distance information for the constraint = F (m) (C) overall evaluation function H (m, λ) = E (m) + λ T F
(M) Here, λ = (λ ₁ ,..., Λ _K ) indicates a Lagrange multiplier for the constraint condition.

(D) m and λ satisfying H = 0 are obtained by an optimization technique.

In the embodiment for realizing the above basic algorithm, corresponding points and the like are defined as follows for convenience.

N corresponding points are set. K constraint conditions are set. Partial derivatives of m with respect to the evaluation function H and the constraint condition F are defined as Hm and Fm as follows.

[0065]

(Equation 10)

The second-order partial derivative of the evaluation function H is defined as Hmm as follows.

[0067]

[Equation 11]

(3) First Embodiment In this embodiment, a calibration method using three views is described. First, the evaluation function E (m) is defined by Expression (18).

[0069]

(Equation 12)

This is an evaluation function for the equivalence of the corresponding points set in each drawing of the three views, and the expression (11)
And the X coordinate values obtained from (13) are equal, and the expression (1)
This is a conditional expression for making the Y coordinate values obtained from 2) and (11) equal and the Z coordinate values obtained from Expressions (13) and (12) to be equal.

The optimization method includes a repetitive gradient method,
In particular, a gradient method using a second-order differential value with good convergence is used. In this case, the repetition end condition (convergence condition) is Hm ≒ 0 and F ≒ 0 for the estimation target variable m.

An algorithm for obtaining the conversion coefficient of each drawing image by the second-order differential value gradient method using the above evaluation function will be described below with reference to the flowchart of FIG. Hereinafter, the conversion coefficient of the drawing image to be obtained is referred to as a parameter variable or simply as a parameter.

(Step S1) Initialization Normally, in the optimization method based on the gradient method, an initial value of a parameter is set to an arbitrary value such as a random number. In the present embodiment, considering that the gradient method has a drawback of convergence to a local minimum and an estimation error due to the convergence, an initial value is set as follows so that parameters can be correctly estimated.

Assuming that there is no rotational distortion or scale distortion in the drawing (although it is a raster image, orthogonality, non-rotation and equal magnification of each axis are preserved as in the CAD diagram), the following relationship is assumed: Set the expression.

[0075] m ⁱ ₀₀ = m ⁱ ₁₁ (magnification _{^{condition) m i 01 = m i 10}} = 0 ( non-rotating and quadrature Conditions) actual distance information between the corresponding points is minimum one set for the drawing L referring to the equation (14) based on, m by the following equation ₀₀
Set the value of ⁱ .

[0076]

(Equation 13)

Since the initial value of λ does not significantly affect the convergence, it is set by a random number.

(Step S2) Value Calculation The values of Hm and F are numerically calculated by the following equation.

[0079]

[Equation 14]

(Step S3) Convergence Judgment If Hm and F are equal to or smaller than specified values (preset convergence conditions), it is determined that the parameters can be estimated, and the process is stopped. Further, the remaining conversion coefficients are obtained from Expressions (5) to (7).

(Step S4) Calculation of Update Amount When the convergence determination is non-convergence, the update amounts dm and dλ of each parameter are numerically calculated by the following equations.

[0082]

(Equation 15)

(Step S5) Update Each parameter value is updated according to the following equation, and the update is performed again (Step S5).
Return to 2).

[0084]

(Equation 16)

(4) Second Embodiment In this embodiment, a calibration method using a two-view drawing will be described. Note that three combinations of (front view, side view), (side view, top view), and (top view, front view) can be considered as a combination of the two views, but in the present embodiment, for convenience (front view, side view) FIG. 2), the calibration method is essentially the same for other combinations.

In the case of a front view and a side view, equations (11) and (1)
2) From the corresponding point on the drawing, only the equivalence with respect to the Y coordinate is obtained (similarly, only the equivalence with respect to the X coordinate is obtained from the side view and the top view, and the X coordinate is obtained from the top view and the front view).
Therefore, only the equivalence for the Y coordinate is set in the evaluation function E. Further, in the affine transformation equations of equations (11) and (12), the equal-magnification projection condition of each axis (in the front view, the X-axis and the Y-axis are projected at the same scale value) and the equiangular rotation projection condition (In the case of a front view, the X axis and the Y axis are rotationally projected while maintaining the orthogonality), so that all the conversion coefficients can be obtained.

The mathematical expression of the same-size projection condition and the equal-angle rotation projection condition in the affine transformation equation is as follows.

In the equation (11), m ₀₀ ¹ = m ₁₁ ¹ and m ₀₁ ¹ = −m ₁₀ ¹ (20) In the equation (12), m ₁₁ ² = m ₀₀ ² and m ₁₀ ² = −m ₀₁ ² (21) equation (20) and (21), in the case of two views, transform coefficients to be determined is the four ^{_{m 10 1, m 11 1,}} m 00 2, m 01 2. A 4 × 1 matrix (transform coefficient matrix) in which the four transform coefficients are arranged is defined as m again.

M = (m ₁₀ ¹ , m ₁₁ ¹ , m ₀₀ ² , m ₀₁ ² ) The evaluation function E (m) based on the equivalence to the TY coordinate is defined by the following equation.

[0090]

[Equation 17]

In addition, in equation (14), equation (20),
Considering (21), the constraint condition f is defined by the following equation.

[0092]

(Equation 18)

In the present embodiment, as in the first embodiment, a gradient method using a second-order differential value is used as an optimization method.

An algorithm for obtaining the conversion coefficient of each drawing image by the second-order differential value gradient method using the above evaluation function will be described below with reference to the flowchart of FIG.

(Step S11) Initialization As in the first embodiment, an initial value is set by equation (19) so that parameters can be correctly estimated. Note that the initial value of λ is set by a random number.

(Step S12) Value Calculation The values of Hm and P are numerically calculated by the following equation.

[0097]

[Equation 19]

(Step S13) Convergence Judgment If Hm and P are equal to or smaller than the specified values, it is determined that the parameters can be estimated and the processing is stopped. Equations (20) to (20)
The remaining conversion coefficients are obtained from (21) and equations (5) to (7).

(Step S14) Calculation of update amount When the convergence condition is non-convergence, the update amounts dm and dλ of each parameter are numerically calculated by the following equations.

[0100]

(Equation 20)

(Step S15) Update Each parameter value is updated according to the following equation, and the update is performed again (Step S1).
Return to 2).

[0102]

(Equation 21)

[0103]

As described above, according to the present invention, since the calibration is performed based on the distance information between the corresponding points on the drawing image, the following effects are obtained.

(1) Since it is not necessary to calculate three-dimensional coordinate values for all corresponding points from a design drawing or the like in which dimensions are written, the number of work steps in calibration can be reduced.

(2) Calibration can be executed even for equipment drawings in which dimensions are only partially written.

[Brief description of the drawings]

FIG. 1 is an algorithm flowchart (part 1) showing an embodiment of the present invention.

FIG. 2 is an algorithm flowchart (part 2) showing the embodiment of the present invention.

FIG. 3 is a drawing image example.

FIG. 4 is a diagram showing a relationship between a point in a three-dimensional space and a point projected on the drawing.

Claims (5)

[Claims] 1. A calibration for obtaining a conversion coefficient of a conversion function for associating a point on a drawing image of a device with the coordinates of a point in a three-dimensional space, and creating a three-dimensional model of the device from the drawing image using the conversion function In the calibration, a projection point in which a point in a three-dimensional space of the device is projected on a three-view drawing of the device is set as a corresponding point, and an image is formed based on distance information between the corresponding point and the corresponding point. A method for calibrating a drawing image, wherein an upper point is associated with a coordinate of a point in a three-dimensional space. 2. An evaluation function in which the equivalence of coordinate values in a three-dimensional space obtained from the corresponding points and the distance between the corresponding points are defined as constraints, and the evaluation function satisfying the constraints is defined. 2. The drawing image calibration method according to claim 1, wherein the conversion coefficient for minimizing a function value is obtained by an optimization method. 3. The optimization method is based on an evaluation function for the equivalence of the corresponding points set in each of the three views,
3. The method according to claim 2, wherein the conversion coefficient of each drawing image is obtained by a second-order differential gradient method. 4. The optimization method according to claim 1, wherein an evaluation function for the equivalence obtained by setting the equal-magnification projection condition and the equiangular rotation condition of the two views to the corresponding point set in the two views is used. The method according to claim 2, wherein the conversion coefficient of each drawing image is obtained by a differential value gradient method. 5. A parameter in the second-order differential gradient method is set to an initial value for preventing convergence to a local minimum and erroneous parameter estimation due to the actual distance between corresponding points. Item 5. The method for calibrating a drawing image according to Item 3 or 4.