JP2923069B2 - Viewpoint position determination method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a viewpoint position determining method for determining a relative positional relationship between two different viewpoints.

[0002]

2. Description of the Related Art First, a conventional method for determining a relative position between two different viewpoints will be described. Next, the principle of stereo image measurement used in the conventional method and the nature of its error will be described. The handling of errors in this conventional method will be described.

(1) Conventional method for determining relative positional relationship between two different viewpoints FIG. 4 shows a relative positional relationship between _two viewpoints O ₁ and O ₂ in a three-dimensional space. When representing the first coordinate system at viewpoint O ₁ (first viewpoint coordinate system) with x ₁ y ₁ z ₁ coordinate system, the coordinate system about the z ₁ axis theta, about the y ₁ axis φ , after performing rotation ψ about the x ₁ axis, translation Δx in the three directions along the new axis, [Delta] y, result of performing Δz second coordinate system in the view point O ₂ (second viewpoint Coordinate system). The second viewpoint coordinate system in FIG. 4 are represented by x ₂ y ₂ z ₂ coordinate system. Here, the relative positional relationship between the first viewpoint O ₁ and the second viewpoint O ₂ is represented by the above-described coordinate conversion parameters θ, φ, ψ, Δx, Δy, Δz.

Conventionally, when determining the relative positional relationship between the two viewpoints O _1, O _2, for n (n ≧ 3) pieces of the measurement points in the three-dimensional space, each of these viewpoints O _1, O ₂ Is measured from each of the positions by stereo image measurement, the observed coordinates of the measured point are represented by a coordinate system at the viewpoint, and determined from the result obtained for each measured point.

In FIG. 5, first and second viewpoints O ₁ and O _{2 are shown.}
The result of measuring the k-th measured point P _k among the n measured points from is expressed in the coordinate system at the viewpoint.

[Outside 1] Expressed by Then the vector

[Outside 2] _Are the viewpoints O ₁ ,
It represents the measurement coordinate vector in O _2.

By the way, if an operator for coordinate conversion from the first viewpoint coordinate system to the second viewpoint coordinate system is represented by T,

(Equation 1) Should hold. By measuring the positions of all the n measurement points from the two viewpoints O ₁ and O ₂ , T in the equation (1) can be determined, and the distance between the _two viewpoints O ₁ and O ₂ can be determined. The relative positional relationship can be determined.

However, in actual measurement, it is not possible to prevent occurrence of an error. Generally, the result of measuring the measured point P _k from each viewpoint O ₁ , O ₂

[Outside 3] Are not coincident in the three-dimensional space and are shifted. This displacement is represented by the displacement vector

[Outside 4] Will be represented using. _Considering that the result of measuring the measured point P _k from the first viewpoint O ₁ is represented by a coordinate system at the second viewpoint O ₂ , from the definition of the coordinate transformation operator T,

(Equation 2) Holds, the displacement vector is

(Equation 3) Holds.

Therefore, in the conventional method, the shift amount vector is determined for all of the n measured points.

[Outside 5] Find the Euclidean norm of (k = 1,2, ..., n),
The sum of the squares of the Euclidean norm is shifted by the evaluation amount E
Then, the relative positional relationship between the _two viewpoints O ₁ and O ₂ is determined by obtaining an operator T for coordinate conversion that minimizes the displacement evaluation amount E.

At this time, since the magnitude of the measurement error is different for each point to be measured P _k , the difference in the magnitude of the error is taken as a weight, and the deviation evaluation amount E is calculated.

(Equation 4) Attempts have been made to improve the accuracy of the determination of the relative positional relationship by determining the relationship (Robert M. Haralick et al., "Pose
Estimation from Corresponding Point Data ", IEEE Tr
ans.on Systems, Man. and Cybernetics, Vol.19, No.
6, PP. 1426-1446). ‖… ‖ Is Euclid
Represents a norm, and W _k is a weight coefficient for a measurement error at the k-th measured point P _k .

(2) Stereo Image Measurement Next, the principle of stereo image measurement will be described with reference to FIG. Stereo image measurement is a method in which a three-dimensional space is projected onto a two-dimensional plane by two left and right cameras provided at the viewpoint, and the position of a point to be measured is measured by parallax between the two cameras. X, y, z as coordinates representing a three-dimensional space
And u and v are used as coordinates representing the position on the two-dimensional image planes 2 and 3 obtained by projecting this three-dimensional space by the two right and left cameras. It is assumed that the x-axis and the u-axis, the z-axis and the v-axis are respectively parallel, and the y-axis is parallel to the optical axis 1 of the camera. Also, the origin O of a three-dimensional space coordinate system (xyz coordinate system)
From the viewpoint. If the distance between the left and right cameras is 2a,
Principal point O _L, the O _R coordinates of each camera, Zorezore (-a, 0,0),
(a, 0,0). Also, the principal point O _L of each camera, the distance between the O _R and the image plane 2, 3 and f. Hereinafter, the left and right images are represented by subscripts L and R, respectively.

[0011] 1 point P in the three-dimensional space (x, y, z) is a point I _L on the left and right image planes _{2,3 (u L, v L)} , I R (u R, v R) to It is assumed that each is projected. At this time, from the epipolar condition, v _L
And v _R have the same value, and are represented by v without distinguishing between them. △ since the I _L I _R P and △ O _L O _R P is similar,
Using the measured values u _L , u _R , v on the image plane, a point P (x, y, z)
_{Is, x = a (u L +} u R) / (u L -u R) ... (3) y = 2af / (u L -u R) ... (4) z = 2av / (u L -u R) ... (5). Stereo image measurement is performed according to the above principle.

FIG. 7 shows the configuration of an example of an apparatus for performing such stereo image measurement. This device is based on digital image processing and has two left and right TV cameras 4
_1, 4 ₂ in the captured image is being scanned for each scan line, it is converted into time-sequential image signal. Each image signal is input to the digitizer 5, sampled by a sampler in the digitizer 5 into several hundred pixels each of which is arranged two-dimensionally like a grid in the vertical and horizontal directions, and further A / D in the digitizer 5. The data is quantized by the converter to several hundred gradations corresponding to the amount of light incident on each pixel. As described above, the image is digitized via the digitizer 5, and is input to the image memory 6 and stored as coordinate information indicating the position of the pixel. Then, it is input to a computer (CPU) 7,
Coordinate measurement values u _L ,
u _R , v is determined. After that, the point P (x, y, z) is obtained by the above equations (3) to (5).

Next, the nature of the error in the stereo image measurement will be described. Since it is possible to set the camera with a position accuracy that satisfies the stereo image measurement using a level, etc., here, the position measurement accuracy of the projection point on the image plane and the position in the three-dimensional space Consider the relationship with decision accuracy. For simplicity, it is assumed that the measurement errors of u _L , u _R , v have the same statistical properties, and their standard deviation is σ. From the propagation law of the error, the standard deviations σ _x , σ _y , σ _z of x, y, z obtained by Expressions (3) to (5) are

(Equation 5) It is represented as

Typically, the standard full viewing angle of a camera is 50 °
Y or less, and the measurement target is mainly near the ground surface, so that y≫x〜z. Therefore, the distance (x ² + y ² + z ² ) ^1/2 from the viewpoint to the measurement target can be approximated by y. Therefore, from Equations (6) to (8), the error increases in proportion to the distance in the x-axis direction and the z-axis direction, that is, in the left-right and up-down directions, whereas the error increases in the y-axis direction, that is, the depth direction. It can be seen that it increases in proportion to the square of. For this reason, in the stereo image measurement, there is a property that the measurement accuracy particularly in the depth direction is significantly reduced as the distance from the viewpoint to the measurement target increases.

(3) Error Handling in Conventional Method for Determining Relative Position Relation between Two Different Viewpoints Generally, the relative position relation between two coordinate systems in a three-dimensional space is determined by three rotation parameters and three parallel parameters. The movement (translation) parameter can be completely described. On the other hand, stereo image measurement is performed by using a level or the like so that the principal axis connecting the principal points of the two left and right cameras and the optical axis of each camera maintain horizontal accuracy of mrad or less. be able to. Therefore, it is realistic to make an assumption that two different viewpoints are in the same horizontal plane. In the following discussion, it is assumed that this assumption is satisfied.
The case of dimension (when the coordinate system at each viewpoint can be described by a two-dimensional coordinate system in a horizontal plane) will be handled.

From the first viewpoint, the k-th point P _k to be measured is measured, and the measurement result in the coordinate system (first viewpoint coordinate system) at the first viewpoint is obtained.

[Outside 6] And the measured coordinate vector in the first viewpoint coordinate system is

(Equation 6) And Similarly, the measured point P _k is measured from the second viewpoint, and the measurement result in the coordinate system (second viewpoint coordinate system) at the second viewpoint is obtained.

[Outside 7] And the measured coordinate vector in the second viewpoint coordinate system is

(Equation 7) And Further, a measurement result viewed from the first viewpoint, represented by a vector in the second viewpoint coordinate system, is referred to as a virtual coordinate vector in the second viewpoint coordinate system,

(Equation 8) Expressed by At this time,

[Outside 8] And (x _{2, k} ', y _{2, k} ')

(Equation 9) Holds. Here, θ, Δx, and Δy are two-dimensional coordinate conversion parameters. In this case, the deviation evaluation amount E is calculated by the equation (4).
Than,

(Equation 10) It is expressed as

[0017] As described above, in stereo image measurement, since inverse proportion to the measurement accuracy decreases to the square of the viewpoint and the distance between the measured point, considered as a reference for the reliability of this, the weight W _k

[Equation 11] Determined as follows. Then, θ, Δ that minimizes E in equation (9)
x and Δy are determined by the least squares method. That is,

(Equation 12) Thus, coordinate conversion parameters that satisfy the following conditional expressions (10) to (12) are determined.

(Equation 13)

When equations (10) to (12) are simultaneously solved for θ, Δx, Δy, θ, Δx, Δy are

[Equation 14] become that way. here,

(Equation 15)

(Equation 16) It is.

As described above, the coordinate conversion parameters θ, Δx, Δy are obtained, and the relative positional relationship between two different viewpoints can be determined.

[0020]

The above-described conventional viewpoint position determination method does not consider the anisotropy of the error in the stereo image measurement, and simply uses a simple weighted average on the assumption that the error is isotropic. Accordingly, there is a problem in that the relative positional relationship between two different viewpoints is determined, so that the accuracy of determining the relative positional relationship cannot be sufficiently obtained.

An object of the present invention is to perform stereo image measurement at each viewpoint to determine the relative positional relationship between two different viewpoints with high accuracy when determining the relative positional relationship. It is to provide a decision method.

[0022]

A first viewpoint position determining method according to the present invention uses n (where n ≧ n) by measuring a stereo image.
2) measuring the position of each of the measured points in the two-dimensional plane from a first viewpoint, and performing stereo image measurement in the respective two-dimensional planes of the n measured points. Measuring the position at from the second viewpoint, the second
And a coordinate conversion parameter describing a relative positional relationship in a two-dimensional plane between the first viewpoint and the second viewpoint for each of the n measurement points;
Calculating the probability density distribution including the true position of the measured point as a variable, calculating the combined probability density distribution by combining the probability density distributions for the first viewpoint and the second viewpoint, A third step of calculating the maximum value of the combined probability density distribution as a function of the coordinate conversion parameter, and calculating the measurement point combining probability by combining the maximum values of each of the n measured points; A fourth step of obtaining the coordinate conversion parameter that maximizes the measurement point synthesis probability.

A second viewpoint position determining method according to the present invention comprises a first step of measuring the positions of n (where n ≧ 3) measured points from a first viewpoint by stereo image measurement. A second step of measuring the respective positions of the n measured points from a second viewpoint by stereo image measurement, and the first step for each of the n measured points.
Calculating a probability density distribution including, as variables, a coordinate conversion parameter describing a relative positional relationship in a three-dimensional space between the viewpoint and the second viewpoint, and the true position of the measured point; Calculating a combined probability density distribution by combining the probability density distributions for a first viewpoint and the second viewpoint;
A third step of calculating a maximum value of the composite probability density distribution as a function of the coordinate transformation parameter, and calculating a measurement point synthesis probability by synthesizing the maximum values of each of the n measured points; A fourth step of obtaining the coordinate transformation parameter that maximizes the measurement point synthesis probability.

[0024]

For each of the n measured points, a coordinate conversion parameter describing the relative positional relationship between the first viewpoint and the second viewpoint and the true position of the measured point are included as variables. A probability density distribution is calculated, the probability density distribution is combined with respect to the viewpoint and the point to be measured, and calculated as a function of a coordinate conversion parameter. Since the relative positional relationship between the viewpoints is determined, the anisotropy of the error is included in the probability density distribution, so that the relative positional relationship in consideration of the anisotropy of the measurement error can be obtained.

[0025]

Next, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is a flowchart showing a procedure of a viewpoint position determining method according to an embodiment of the present invention, FIG. 2 is an explanatory diagram showing a relative positional relationship between viewpoints, and FIG. It is an explanatory view showing the result.

Before describing the specific procedure of the method for determining the viewpoint position according to the present embodiment, first, the probability density distribution of errors in stereo image measurement will be described, and then the specific procedure will be described.

(1) Error probability density distribution Between the measured values u _L , u _R , v on the image plane obtained by stereo image measurement and the coordinates (x, y, z) of the point P to be measured are as described above. Equation (3)-
(5) _{from, u L = (x + a} ) f / y ... (13) u R = (x-a) f / y ... (14) v = zf / y ... (15) the relationship is established. Here, considering the total derivatives of equations (13) to (15),

[Equation 17] Becomes Here, dx, dy, and dz are measured points P, respectively.
3 shows measurement errors in the x, y, and z directions of the coordinates.

In the stereo image measurement, it is clear that the error does not affect each other between the left and right image planes and between the horizontal direction and the vertical direction in one image plane. du _L , du _R , and dv are considered to be independent. Here, it is assumed that the measurement errors on the image plane respectively follow the normal distribution of the standard deviation σ. In the measurement on the image plane, it is not inconceivable that the standard deviations σ _u , σ _v in the horizontal direction and the vertical direction are different from each other, but here, for simplicity, σ _u , σ _v are equal. Is represented by σ. Incidentally, the standard deviation σ is a system-specific value determined by a measurement system for stereo image measurement, that is, an optical system or an image measurement algorithm. Here, the measurement errors du _L , du _R , dv on the image plane
Are the probabilities that occur simultaneously, the probability density distribution Φ is

(Equation 18) Given by By substituting the above equations (16) to (18) into the equation (19), the probability density distribution, which is the probability that the errors dx, dy, dz in the three-dimensional space occur simultaneously, is calculated. This probability density distribution has an error d in a three-dimensional space.
It is represented by a function form including anisotropy of x, dy, dz.

(2) Method of Determining Viewpoint Position As described above, the relative positional relationship between two coordinate systems in a three-dimensional space includes three rotation parameters θ, φ, ψ and three translational (translation) parameters. By Δx, Δy, Δz,
Can be completely described. On the other hand, in stereo image measurement, the level of the principal axis connecting the respective principal points of the two left and right cameras and the optical axis of
The following horizontal accuracy can be maintained. Considering the features of the stereo image measurement described here, first, in a two-dimensional case (at each viewpoint, the xy plane in the coordinate system at the viewpoint is considered to be horizontal, and the distance between two different viewpoints is determined based on the horizontal plane). (Only the relative positional relationship in the horizontal plane is obtained).
It is easy to extend this argument to the three-dimensional case.
In the case of two-dimensional handling, the error dv in the vertical direction on the image plane is negligible.

[Equation 19] It is transformed as follows.

First, n in a two-dimensional space (where n ≧
2) First viewpoint O ₁ for each of the measured points
Stereo image measurement from the measures the coordinate system the coordinates of the (first viewpoint coordinate system) with expressed was that the measuring point for the first viewpoint O _1. Here, n ≧ 2, because it is two-dimensional, the position of a point cannot be determined unless two points are given and the distance to the two points is determined. The measured coordinates of the _k- th (where 1 ≦ k ≦ n) measurement point P _k is

[Outside 9] (Step 101). Next, similarly, for each of the n measurement points, a stereo image measurement from the _second viewpoint O _{2 is performed} to represent the n measurement points in the coordinate system (second viewpoint coordinate system) for the second viewpoint O _2. The coordinates of the measured point are measured. The measured coordinates of the k-th measured point P _k

[Outside 10] (Step 102).

Here, the measured coordinate vector of the k-th measured point P _k viewed from the i- _th viewpoint O _i (i = 1, 2) is

(Equation 20) Expressed by FIG. 2 shows the relative positional relationship between the _first and second viewpoints O ₁ and O ₂ . Here, the true coordinates of the measured point P _k in the first viewpoint coordinate system are represented by (x _{1, k} , y _{1, k} ), and the true coordinate vector in the first viewpoint coordinate system is

(Equation 21) And Similarly, the true coordinates of the measured point P _k in the second viewpoint coordinate system are represented by (x _{2, k} , y _{2, k} ), and the true coordinate vector in the second viewpoint coordinate system is

(Equation 22) And When an operator representing coordinate transformation from the first viewpoint coordinate system to the second viewpoint coordinate system is represented by T,

(Equation 23) Holds. That is, (x _{2, k} , y _{2, k} ) = T (x _{1, k} , y _{1, k} ) holds. The coordinate conversion parameter represented by the operator T is θ,
Assuming that Δx, Δy, this equation is expressed as x _{2, k} = x _{1, k} cos θ + y _{1, k} sin θ -Δx (22) y _{2, k} = -x _{1, k} sin θ + y _{1, k} cos θ−Δy (23)

Measurement coordinate vector in the first viewpoint coordinate system

[Outside 11] And the true coordinate vector

[Outside 12] Is

(Equation 24) Causes only an error. The probability density distribution Φ of the error
_From Equation (20), _{1, k} is

(Equation 25) It is expressed as here,

(Equation 26) It is. Similarly, the measurement coordinate vector in the second viewpoint coordinate system

[Outside 13] And the true coordinate vector

[Outside 14] And

[Equation 27] When only the error occurs, the probability density distribution Φ of the error
_{2, k} is

[Equation 28] Becomes here,

(Equation 29) It is.

From the above equation (21), the true coordinate vector in the second viewpoint coordinate system is obtained.

[Outside 15] Is the true coordinate vector described in the first viewpoint coordinate system using the operator T

[Outside 16] Can be converted to If the coordinate transformation parameters θ, Δx, and Δy are collectively represented by t, the probability density distribution Φ _{2, k} (x _{2, k} , y _{2, k} ) in the second viewpoint is (x _{1, k} , y _{1, k} , t).

For each measured point P _k (1 ≦ k ≦ n),
The inter-view combined probability density distribution F _k (x _{1, k} , y _{1, k} , t) is a probability distribution in which the errors represented by the equations (24) and (25) occur simultaneously.
From the equation of the synthesis of the known error density distribution,

[Equation 30] It is represented by Where g _k (x _{1, k} , y _{1, k} , t) is

(Equation 31) (Step 103).

Next, the inter-view combined probability density distribution F _k (x _{1, k} ,
y _{1, k,} a t) (x _{1, k,} the maximum value when viewed as a function of y _{1, k),} as the maximum value of t function s _k (t),

(Equation 32) Ask like. That is, for a certain t, x _{1, k} , y
The maximum value of the inter-view combined probability density distribution F _k when only _{1, k} is changed is determined. Obviously, the time when F _k is maximized is when g _k (x _{1, k} , y _{1, k} , t) is minimized, so that g _k (x _{1, k} , y _{1, k} , t) ) Is the minimum coordinate vector

[Outside 17] Is calculated _{, and} F _k (x _{1, k} , y _{1, k} , t) at that time is calculated.
The coordinate vector is, of course, a vector displayed in the first viewpoint coordinate system.

Here, how to find the condition that minimizes g _k (x _{1, k} , y _{1, k} , t) will be described.

[Equation 33] From the above, a coordinate vector minimizing g _k (x _{1, k} , y _{1, k} , t)

(Equation 34) Should be obtained. From equation (29),

[Outside 18] With respect to the following two conditional expressions (30) and (31),

(Equation 35) Is obtained. here,

[Equation 36]

(37) It is. By simultaneous equations (30) and (31),

[Outside 19] Solving for

(38) Is obtained. Expressions (30) and (31)

[Outside 20] Is substituted into equation (26) to obtain the maximum value s _k (t) which is a function of t (step 104).

By the way, the maximum value s _k (t) which is a function of t
Is a function representing the probability density distribution of the error with respect to t according to the definition equation (28). Therefore, n measured points P _k (1
≦ k ≦ n), the probability density distribution of the error can be synthesized. Assuming that the synthesized probability density distribution is a measurement point synthesis probability S (t), from a known synthesis formula,

[Equation 39] It is. Therefore, the measurement point combination probability S (t) is obtained (step 105).

Since the measurement point synthesis probability S (t) is a probability density distribution, t that maximizes S (t) is the maximum likelihood value of t. So next,

[Outside 21] The coordinate transformation parameter t (= θ, Δx, Δy) which gives the following equation may be obtained, and the coordinate transformation parameter t indicates the relative positional relationship between the first viewpoint and the second viewpoint. θ,
S (t) is calculated by changing Δx and Δy little by little, and a coordinate conversion parameter t (= θ, Δx, Δ
y) may be obtained (step 106). Or the expression
Like (29),

(Equation 40) , The coordinate conversion parameter t may be obtained analytically.

Next, regarding the result of implementing this embodiment,
This will be described with reference to FIG. 3 while comparing the result with the conventional method. The distance 2a between the left and right cameras is 1 m, and the focal length (ie, the distance between the principal point and the image plane) f is 1 for each camera.
With a 6.1mm lens attached and stereo image measurement,
From each of the first and second viewpoints O ₁ and O ₂ , the coordinates of four measured points in a two-dimensional plane were measured. Table 1 shows the results. Note that when the relative positional relationship between the _first and second viewpoints O ₁ and O ₂ was actually measured, the true coordinate conversion parameters were θ = 87.40 °, Δx = 37.45 m, and Δy = −.
It was 26.37 m. Further, shown by the solid line in FIG. 3 the coordinate system in the real second viewpoint O _2. In addition, each viewpoint O ₁ ,
The measured position of each measured point from O ₂

[Outside 22] Expressed by

[Table 1]

Using this measurement result, the coordinate conversion parameters were calculated by the method of the present embodiment described above.
θ = 87.69 °, Δx = 36.18 m, Δy = −25.4
3 m were obtained. The error from the true coordinate transformation parameters is 0.29 ° for θ and 1.27 for Δx.
m and Δy are 0.94 m. The position of the second viewpoint calculated at this time is represented by O ₂ ′ in FIG.
The coordinate system at the viewpoint O ₂ ′ of FIG.

On the other hand, when the coordinate conversion parameters were calculated by the conventional method using the weighted average described in [Prior Art], θ = 81.52 ° and Δx = 35.78.
m, Δy = -21.69 m were obtained. The errors from the above coordinate transformation parameters are 5.88 ° for θ, 1.67 m for Δx, and 4.68 m for Δy. The position of the second viewpoint calculated at this time is represented by O ₂ "in FIG. 3, and the coordinate system at the second viewpoint O ₂ " is represented by a dotted line.

Comparing the above results, the coordinate transformation parameters obtained by the method of the present embodiment described above are about 20 times in θ, about 1.3 times in Δx, and about 1.3 times in Δy, as compared with the conventional method. It can be seen that the 5.0-fold precision is improved, and by using the method of this embodiment,
It can be seen that the relative positional relationship between the _two different viewpoints O ₁ and O ₂ was determined with high accuracy.

Although the embodiment of the present invention has been described for a two-dimensional case, it is easy to extend this to a three-dimensional case. Next, the three-dimensional case will be described focusing on the difference from the two-dimensional case.

In the three-dimensional case, if three points are given and the distance to the three points is not obtained, the position of the point is not determined.
Three or more measurement points are required. Therefore, while n ≧ 2 in the two-dimensional case, n ≧ 3. The coordinate conversion parameters in the three-dimensional case are θ, φ, ψ,
It is completely represented by Δx, Δy, Δz.

For the k-th measured point P _k , the true coordinate vector in the first viewpoint coordinate system and the true coordinate vector in the second viewpoint coordinate system are respectively

[Equation 41] In this case, an expression representing a specific coordinate transformation corresponding to the expressions (22) and (23) is: x _{2, k} = x _{1, k} cos φ cos θ + y _{1, k} cos φ sin θ-z _{1, k} sin φ-Δx (36) y _{2, k} = x _{1, k} (sinψsin φcos θ-cosψsin θ) + y _{1, k} (cosψcos θ + sin φsinψsin θ) + z _{1, k} sinψcos φ-Δy (37) z _{2, k} = x _{1, k} (sinψsin θ + cosψsinφcosθ) + y _{1, k} (cosψsinφsinθ−sinψcosθ) + z1 _{, k} cosψcosφ-Δz (38) Then, using the equation (19) representing the probability density distribution Φ in which the errors du _L , du _R , and dv occur simultaneously, the two-dimensional inter-view combined probability density distribution F _k (x _{1, k} , y _{1, k} , t) instead of equation (26), the three-dimensional combined probability density distribution F _k (x
_{1, k} , y _{1, k} , z _{1, k} , t) may be considered and handled as described above. Where g _k (x _{1, k} , y _{1, k} , z _{1, k} , t)
Is

(Equation 42) It is.

[0046]

As described above, according to the present invention, for each of n measurement points, a coordinate conversion parameter describing a relative positional relationship between a first viewpoint and a second viewpoint,
A probability density distribution including the true position of the measured point as a variable is calculated, and the probability density distribution is calculated with respect to the viewpoint and the measured point as a function of a coordinate conversion parameter,
By calculating the coordinate transformation parameter that maximizes the combined result, the anisotropy of the error is included in the probability density distribution. Therefore, the relative positional relationship in which the anisotropy of the error is considered can be obtained. There is an effect that the relative positional relationship can be determined with high accuracy.

[Brief description of the drawings]

FIG. 1 is a flowchart showing a processing procedure of a viewpoint position determining method according to an embodiment of the present invention.

FIG. 2 is an explanatory diagram showing a relative positional relationship between viewpoints.

FIG. 3 is an explanatory diagram showing a result of specifically implementing the embodiment of FIG. 1;

FIG. 4 is an explanatory diagram showing a relative positional relationship between _first and _second viewpoints O ₁ and O ₂ .

FIG. 5 is a diagram illustrating a conventional viewpoint position determination method.

FIG. 6 is a diagram illustrating the principle of stereo image measurement.

FIG. 7 is a block diagram showing a configuration of an apparatus for performing stereo image measurement.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 Optical axis 2 Image plane of left camera 3 Image plane of right camera 4 ₁ , 4 ₂ TV camera 5 Digitizer 6 Image memory 7 Calculator 101 to 106 Steps O ₁ First viewpoint O ₂ Second viewpoint

────────────────────────────────────────────────── ─── Continuation of front page (72) Inventor Atsushi Ide 1-6, Uchisaiwaicho, Chiyoda-ku, Tokyo Nippon Telegraph and Telephone Corporation (56) References JP-A-9-326029 (JP, A) JP-A Heisei JP-A-4-256207 (JP, A) JP-A-3-6780 (JP, A) JP-A-60-173403 (JP, A) JP-A-60-171410 (JP, A) A) (58) Fields investigated (Int. Cl. ⁶ , DB name) G01B 11/00-11/30 G01C 3/06 G06T 7/00

Claims (2)

(57) [Claims] 1. A viewpoint position determining method for determining a relative positional relationship between two different viewpoints, the method comprising:
a first step of measuring the position of each of the n (where n ≧ 2) measurement points in a two-dimensional plane from a first viewpoint, and a stereo image measurement to each of the n measurement points A second step of measuring a position in a two-dimensional plane from a second viewpoint, and for each of the n measurement points, a distance between the first viewpoint and the second viewpoint Calculating a probability density distribution including, as variables, a coordinate conversion parameter describing a relative positional relationship on a two-dimensional plane and a true position of the measured point, and calculating the probability density distribution for the first viewpoint and the second viewpoint. A third step of calculating a combined probability density distribution by combining distributions, and calculating a maximum value of the combined probability density distribution as a function of the coordinate conversion parameter; and Combine values and measure Calculating a synthetic probability, determine the coordinate transformation parameters to maximize the measurement point synthetic probability,
A viewpoint position determining method having a fourth step. 2. A viewpoint position determining method for determining a relative positional relationship between two different viewpoints, the method comprising:
A first step of measuring the respective positions of n (where n ≧ 3) measurement points from a first viewpoint, and the respective positions of the n measurement points are determined in a second step by stereo image measurement.
A second step of measuring from the viewpoint, and a relative positional relationship in the three-dimensional space between the first viewpoint and the second viewpoint for each of the n measurement points. A probability density distribution including a coordinate transformation parameter and a true position of the measured point as variables is calculated, and the probability density distributions are combined for the first viewpoint and the second viewpoint, thereby obtaining a combined probability density distribution. A third step of calculating the maximum value of the combined probability density distribution as a function of the coordinate transformation parameter; and combining the maximum values of each of the n measurement points to obtain a measurement point combination probability. And determining the coordinate transformation parameter that maximizes the measurement point synthesis probability.