JPH07139918A - Method for measuring central position/radius of cylinder - Google Patents

Abstract

PURPOSE:To enable highly accurate measurement by obtaining equations of (n) tangents drawn from projection centers of a right and a left cameras to tangent planes of a cylinder, operating an approximate point of a center of the cylinder and calculating arm evaluation function for an area in the vicinity of the approximate point. CONSTITUTION:Projection points on an image surface at the boundary of a cylinder are detected thereby to detect tangent planes of the cylinder. Equations of tangents F1 L1, F2 L2,... drawn from projection centers F1, F2,... of a right and a left cameras for obtaining a stereo image to the tangent planes of the cylinder are determined. A center C of the cylinder is operated based on the obtained equations as an approximate point of a true center of the cylinder. Then, based on the equations of tangents, a square sum of differences between lengths of perpendiculars CL1, CL2,... from coordinates of the virtual center C of the cylinder to the tangents and an average value of the perpendiculars is used as an evaluation function E, and coordinates of an approximate area of the center C are substituted into coordinates of the virtual center C of the cylinder to obtain coordinates where the evaluation function E becomes minimum. The obtained coordinates represent a position of the center of the cylinder. The average length of the perpendiculars to the tangents is a radius of the cylinder.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of measuring the center position and radius of a cylinder by measuring a stereo image on an object having a cylinder shape. This technology
In a position measurement system using stereo image processing,
It is used to obtain the position of a cylindrical object such as a telephone pole with high accuracy.

[0002]

2. Description of the Related Art First, a stereo image measuring method will be described, and then a conventional example in which this method is applied to cylinder measurement will be described.

The principle of stereo image measurement is shown in FIG. X, y, and z are used as the coordinates indicating the three-dimensional space, and u and v are used as the coordinates indicating the position on the image plane. x-axis and u-axis, z
The axis and the v-axis are parallel to each other, and the y-axis is parallel to the optical axis of the camera for obtaining a stereo image. Let O, which is the origin of the spatial coordinate system, be the projection centers F _l , F _{r of the} left and right cameras.
Take the middle point. If the distance between the cameras is 2a, then F _l ,
The coordinates of F _{r in} the three-dimensional space are (-a, 0,
0) and (a, 0, 0). The image plane of the actual camera is on the side opposite to the measurement target with respect to the projection centers F _l and F _r of the camera, but in order to make it easy to see the geometrical quantitative relationship described below, in FIG. On the same side, the positions are symmetrical with respect to the projection centers F _l and F _r . At this time, the distance between the projection centers F _l and F _r and the image plane is f
Then, the three-dimensional spatial coordinates of the image origins O _l and O _{r on} the image planes of the left and right cameras are (−a, f,
0) and (a, f, 0). Hereinafter, l and r are used as subscripts indicating left and right images, and the origin O is referred to as a viewpoint.

Now, it is assumed that the point P in the three-dimensional space is projected onto the points I _l (u _l , v _l ) and I _r (u _r , v _r ) on the left and right image planes. In stereo image measurement, I _l and I _r are _displayed on the image.
Is determined, and the three-dimensional space coordinates (x, y, z) of the point P are obtained based on the principle of triangulation. Here, since the optical axes of the two cameras are on the same plane and the x axis and the u axis are parallel to each other, v ₁ and v _r have the same value. Therefore, in the following, both are represented by v without distinction. As shown in FIG. 5, due to the geometrical condition that the straight lines F _l I _l and F _r I _r intersect at the point P, the coordinates u _l , u _r , v on the image plane and the coordinates x in the three-dimensional space are set. , y, the relationship between z _{is, x = a (u l +} u r) / (u l -u r) (1) y = 2af / (u l -u r) (2) z = 2av / (u l −u _r ) (3)

FIG. 6 shows a block diagram of an apparatus configuration for performing such stereo image measurement, taking digital image processing as an example. The images captured by the television cameras 1-1 and 1-2 are converted into temporally continuous video signals while being scanned for each scanning line. This video signal is sampled by a sampler of the digitizer 2 into hundreds of vertical and horizontal pixels per screen like a grid pattern. At the same time, A /
The D converter quantizes the density corresponding to the amount of light incident on each pixel into several hundred gradations. The image looks like this
It is stored in the image memory 3 as information including the coordinates indicating the position of the pixel and the density there. Since the brightness of the object boundary projected on the image plane usually changes greatly, the computer (CPU) 4 performs a differentiating process on the image stored in the image memory 3 to determine the place where the brightness changes. The projected position of the boundary is detected. By performing such processing on the left and right images, corresponding points I _l (u _l , v _l ) and I _r (u _r , v _r ) on the left and right image planes can be obtained. As described above, in the stereo image processing, the image plane coordinates u _l , u _r , and v of the object projection point are measured, and the three-dimensional space coordinate x,
Indirectly measures y and z.

Next, an example in which the above-described stereo image measuring method is simply applied to the measurement of the center position and radius of a cylinder will be described. A stereo image measurement model for a cylinder is shown in FIG. Normally, the xy plane is parallel to the ground surface and horizontal, and the z-axis is parallel to the central axis of the cylinder and vertical, so that FIG.
Consider a two-dimensional measurement on the xy plane as shown in FIG. Figure 7
Is a cylinder A whose longitudinal direction is in the z-axis direction, and v
It is a cross-sectional view taken along the xy plane where = 0, and the quantities relating to the left and right of the cylinder A are represented by subscripts L and R, respectively. In addition, in particular, when it is necessary to distinguish the true value and the measured value, the symbol " ⁰ " for the true value and the symbol "~" for the measured value (however, it is written above the letters in the figure. , In the text preceded by a letter). Now consider the left side of the cylinder projected onto the left camera. If a tangent line is drawn from the point F _l to the cylinder A and the contact point is L _l , the cylinder A
The boundary position of is projected as intersection points u _l , _L of the tangent line F _l L _l and the image plane. Similarly, the projection points of the right cylinder boundary of the left camera and the left and right cylinder boundaries of the right camera are points _ul , _R , and
u _{r, L,} u _r, become _R. Therefore, the left and right positions of the cylinder A are straight lines F _l u _l , _L and F _r u _r , _L and straight lines F _l u _l , _R and F.
_r u _r, the intersection of _{R ~ L (~ x L,} ~ y L), ~ R (~ x R, ~ y R) is measured as a. Based on this measurement result, 2 points ~ L, ~ R
The center of the cylinder is determined to be ~ C (~ x _C , ~ y _C ),
Distance from this center point to point ~ L or ~ R, that is, 2 points
Let 1/2 of the distance between ~ L and ~ R be the radius of the cylinder.

[0007]

The problems of the conventional method for measuring the center position / radius of a cylinder will be described below.
As described above, in stereo image measurement, it is premised that points to be measured in space can be observed by the left and right cameras. However, when measuring a cylinder, there is a problem that this assumption does not hold because the contact surface of the cylinder projected on the image plane differs between the left and right cameras. Therefore, the two points ~ L, ~ R obtained from different contact surfaces are not on the circumference and the correct cylinder boundary position cannot be measured. As a result, these 2 points ~ L, ~ R
The cylinder radius determined as the distance different from the true value, also the center point of the cylinder determined as the center of two points ~ _C (~ x C, ~
y _C ) does not coincide with the true center position C ⁰ (x _C ⁰ , y _C ⁰ ),
As shown in FIG. 7, the distance between the two points (˜C, C ⁰ ) will occur as a center position measurement error. In this way, when stereo image measurement is applied to a cylinder, a systematic error will occur. Next, this error will be examined.

Now, the straight lines F _l u _l , _L , F _l u _l , _R , F _r u _r , _L ,
F _r u _r, represents the amount relating to _R each subscript 1,2,3,4, the slope of these straight lines respectively _{m 1, m 2, m 3} , m 4
And The value is the geometric relationship between these _{m i (i = 1~4),} m 1 = f / u l, L, m 2 = f / u l, R, m 3 = f / u r, L, m ₄ = f / u _r , _R (4) As mentioned above, f is the focal length of the camera. In this case, the equations of the above four straight lines are: y = m ₁ (x + a) (5) y = m ₂ (x + a) (6) y = m ₃ (x−a) (7) y = m ₄ It can be expressed as (x-a) (8). Therefore, (5), (7) and (6),
From (8), the coordinates (~ x _L , ~ y _L ) of the intersection points ~ L, ~ R, (~
x _R , ~ y _R ) are as follows.

~ X _L = -a (m ₁ + m ₃ ) / (m ₁ -m ₃ ) (9) ~ y _L = -2am ₁ m ₃ / (m ₁ -m ₃ ) (10) ~ x _R = −a (m ₂ + m ₄ ) / (m ₂ −m ₄ ) (11) to y _R = −2 am ₂ m ₄ / (m ₂ −m ₄ ) (12) Here, as an example, the camera interval is 50 cm, and the cylinder is When the radius is 15 cm, (~ x _L , ~ y _L ) and (~ x _R , ~ y _R ) are calculated for 0 <x _C ⁰ <0.5 m and 0.2 <y _C ⁰ <1 m, and the measurement error FIG. 8 shows the result of finding the distance between two points (˜C, C ⁰ ). FIG. 8 is a three-dimensional representation of the distance (measurement error) between two points (~ C, C ⁰ ), x _C ⁰ , y _C ⁰ as three axes. From this figure, the cylinder approaches the viewpoint. It can be seen that the measurement accuracy deteriorates as it goes on.

The present invention has been made in order to solve such a problem, and an object thereof is to provide a method for calculating the center position and radius of a cylinder with high accuracy by processing a stereo image. is there.

[0011]

In order to achieve the above object, a method of measuring the center position and radius of a cylinder according to the present invention is a method of measuring the center position and radius of a cylindrical object using stereo image processing, A first step of computing a stereo image to detect a tangential surface of a cylinder from the image, and a second step of obtaining an equation of n tangent lines drawn from the projection center of a camera for obtaining the stereo image to the tangential surface of the cylinder. And the length p _{i of the} perpendicular line drawn from the coordinates of the virtual center of the cylinder to each of the tangent lines based on the equation of the tangent line and the average value of these perpendicular lines ⁻ p
The sum of squares of the difference E = Σ _{i = 1} ⁿ (p _i − ⁻ p) ² is used as the evaluation function, and the coordinates of the virtual center are changed to obtain the value of the coordinates at which the evaluation function E is minimized. The third step is to set the center position and to obtain the average value of the lengths of the perpendiculars drawn to the tangent lines at this time to obtain the radius, and a third step.

[0012]

In the cylinder center position / radius measuring method of the present invention, with respect to n tangent lines drawn from the projection centers of the left and right cameras on the tangential surface of the cylinder detected from the image by processing the stereo image,
Taking advantage of the fact that the sum of squares of the difference between the length of a perpendicular line drawn from an arbitrary point and the average value of these tangents is the minimum from the center of the cylinder, the arbitrary point is taken as the virtual center of the cylinder. By changing the coordinates of the virtual center and setting the coordinates at which the above sum of squares is the minimum as the center position of the cylinder, and obtaining the average value at that time as the radius, stereo image measurement is performed at the center position of the cylinder.
Avoid systematic errors that occur when applied to radius measurement.

[0013]

Embodiments of the present invention will now be described in detail with reference to the drawings.

FIG. 1 is a flow chart showing a basic embodiment of the present invention. This embodiment consists of four steps. First, in step 1, the stereo image is arithmetically processed to measure the image plane projection point at the cylinder boundary, and the tangential surface of the cylinder is detected. Next, in step 2, the equation of the tangent line drawn to the tangent surface of this cylinder from the projection centers of the left and right cameras for obtaining a stereo image is determined. Next, in step 3, the center of the cylinder is calculated by the conventional method based on the obtained tangential equation, and this is set as an approximate point of the true center of the cylinder. Next, in step 4, the sum of squares of the differences between the lengths of the perpendiculars drawn from the coordinates of the virtual center of the cylinder to the respective tangents based on the equation of the tangents obtained above and the average values of these perpendiculars is an evaluation function. E, substitute the coordinates of the area near the center of the cylinder into the coordinates of the virtual center of the cylinder, obtain the value of the coordinates at which the evaluation function E becomes the minimum, and set it as the center position of the cylinder.
At this time, the average value of the lengths of the perpendiculars drawn to the tangents is calculated and used as the radius.

In this embodiment, the coordinates of the virtual center point C of the cylinder are (x _C , y _C ), and the evaluation function E is the length p _i (i = _i ) of the perpendicular line drawn from the point C to the four tangent lines. and 1-4), the average value of the lengths of these perpendiculars ^- p (= (1/4) ^Σ
_{j = 1} ⁴ p _j , where j = 1 to 4 and p _i and p _j are the same), that is, E = Σ _{i = 1} ⁴ {p _i − ⁻ p} ² Consider (13). The value of E becomes the minimum when the virtual center point is the center of the true cylinder. Therefore, the value of the coordinate (x _C , y _C ) that minimizes this evaluation function E is obtained. The symbol Σ _{i = 1} ⁴ in the above equation
Etc. show the sum total of i = 1 to 4 etc. Where the length of the perpendicular p
The relationship between _i and the coordinates (x _C , y _C ) of the virtual center point C is given by p _i = | m _i x _C −y _C + b _i | / √ (m _i ² +1) (14). However, b _i is the coordinate where the tangent intersects the y-axis, and b _i (i = 1 to 4) are m ₁ a, m ₂ a, and
-M ₃ a, a -m ₄ a. Since it is difficult to analytically obtain the condition for minimizing E in Expression (13), the present embodiment obtains the condition as follows. First, in step 3, in the conventional method, that is, as the center of 2 points ~ L, ~ R,
Calculate C (~ x _C , ~ y _C ). Next, in step 4, the coordinates of this point to C are considered to be the approximate points of the true center position C ⁰ , and the value of the neighboring region is actually substituted into (x _C , y _C ) to calculate E, (X _C , y _C ) giving the minimum value of E is obtained as an estimated value (^ x _C , ^ y _C ) of the center position of the cylinder. Further, obtained in this case ^- p, i.e. an average value of the cylinder radius to the value and the estimated value ^ p of the cylinder radius.

Although it takes time, the measurement range can be easily known. Therefore, step 3 is omitted and the coordinates of these measurement range areas are sequentially substituted into the coordinates of the virtual center to calculate E. By doing so, it is possible to similarly obtain the estimated values of the cylinder center position and the cylinder radius.

The present invention will be described below with reference to specific examples.

[Embodiment 1] Now, the distance 2a between the left and right cameras is 20 cm, the focal length of the camera lens is 5 mm, the sampling interval on the image plane having a size of 1 pixel is 10 μm, and the image plane projection point position is measured. The standard deviation of the error is 1 pixel. Also, the radius of the cylinder is 15 cm, and its center position is (0.3
m, 1 m). Through the simulation under such conditions, the above-described embodiment will be specifically described with reference to the flowchart of FIG. In the following, all units of length are m, and this m is omitted below.

First, the measurement of the image plane projection point of the cylinder boundary in step 1 is performed by detecting the position where the brightness changes abruptly by a differentiating process or the like. Shunji Mori, Tsugeko Sakakura, "Basics of Image Recognition [II]",
Details are provided in Ohmsha, 1990. Here, under the above-mentioned simulation conditions, the pixel position of the projection point is calculated geometrically, that is, a tangent line is drawn from the camera projection center to the cylinder, and calculated as the intersection of this tangent line and the image plane. Further, the above-mentioned image plane projection point position measurement error is given to this coordinate value by a normal random number, and a fractional part or less is truncated and digitized. As a result of this calculation, the measurement coordinates of the image plane projection point to u _l , _L ,
The values of ~ u _l , _R , ~ u _r , _L , ~ u _r , _R are 123 and 28, respectively.
It was calculated as 6, 26, 178.

In step 2, the equations of the four tangents are actually determined. The size of one pixel is 10 μm, and the focal length f
Since There is 5 mm, m ₁ is Considering Equation _{(4) m 1 = 4.07 (} = f / u l, L = 5 / (123 × 1
0 ⁻² )), while the intercept b ₁ = 0.41 (= m ₁
a = 4.07 × 0.1). Similarly, m ₂ , m ₃ , m ₄ and b ₂ , b ₃ , b ₄ are 1.7 respectively.
5, 19.23, 2.81 and 0.175, -1.9.
It is calculated as 2, -0.28. This determined the equation of the four tangents.

[0021] In step 3, the tangent of the two-intersection-L, the coordinates of _{~ R (~ x L, ~} y L), (~ x R, ~ y R) is calculated, - the approximate point of it from the cylindrical center C Find (~ x _C , ~ y _C ). The equation (9) ~ (12), (~ x L, ~ y L), (~ x R, ~
The coordinates of y _R are (0.154, 1.031),
It is calculated as (0.430, 0.926). Therefore, the coordinates of the approximate points are (0.292, 0.978) (=
(0.154 + 0.430) / 2, (1.031 + 0.
926) / 2). In this conventional method, this coordinate is used as the center position, and errors of 0.008 and 0.022 occur in this example in the x and y directions, respectively. On the other hand, the value of the radius is 0.149 m, which is obtained accurately.

In step 4, the evaluation function E is calculated for the area near the approximate point, and the coordinates that minimize it are determined as the cylinder center position. Here, the approximate point (0.292, 0.978) obtained in step 3 is used as the center, and in 0.005 steps in both the x and y directions, from 0.242 to 0.
The evaluation function E given by the equation (13) was calculated up to 342 and in the range from 0.928 to 1.028. As a result, (0.302, 1.003) was obtained as the estimated coordinates (~ x _C , ~ y _C ) of the center position of the cylinder that minimizes E. In this case, the error in the x and y directions is 0.0
02, 0.003, which is about 5 to 6 compared with the conventional method.
It was confirmed that the double precision was improved. By reducing the step size, it is possible to obtain a measurement result with higher accuracy. Also, the radius at this time is 0.149,
It was confirmed that the radius was also obtained accurately.

[Embodiment 2] In the above-described Embodiment 1, the case where both sides of the cylinder can be observed has been described as an example, but as shown in FIG. 2, the same can be applied to the case where only one side can observe. That is, the origin is set at an appropriate position on the straight line connecting the projection centers F ₁ , F ₂ , ... And the perpendicular line is drawn from the virtual center point C to the tangents F ₁ L ₁ , F ₂ L ₂ ,. Next, the length of each perpendicular line is calculated from Expression (14), the value of the evaluation function of Expression (13) is calculated, and the position that gives the minimum value may be obtained as the center position. In this case, it is necessary to observe from four or more positions, and the number of tangents is n ≧ 4. In this case, the equation (13) uses E = Σ _{i = 1} ⁿ (p _i − ⁻ p) ² . In this embodiment, since it is not possible to obtain a point near the center of the true cylinder, step 3 in FIG. 1 is omitted.

[Embodiment 3] An embodiment in which the present invention is applied to outdoor work will be described. Automation of outdoor work is currently being considered for reasons such as an improved work environment and rising labor costs. Here, with the aim of automating various operations on the utility pole by remote operation of the manipulator, we will measure the relative position between the stereo camera attached to the tip of the manipulator and the utility pole, and control the position of the manipulator. explain.
There is a method of measuring and controlling the viewpoint position of a cylindrical object such as a telephone pole by using position information of feature points on the surface. This method will be briefly described with reference to FIG. FIG. 3 is similar to FIG. 7, but parts related to the camera are omitted. The characteristic point M on the surface of the electric pole A is θ with the center point C (x _C , y _C ) of the cylinder as the center.
It is located on the rotated circumference, and the coordinates of this point are (x _M ,
y _M ). In addition, as a normal feature point in telephone pole work,
A hole is used to fix the metal fitting that supports the cable to the utility pole.

In the present embodiment, the cylinder center point C is obtained in the same manner as in the first or second embodiment. The feature point M is
Obtained by the stereo image measurement method. In the case of FIG. 3, the following equation is obtained from the geometrical relationship.

X _M = x _C + ps in θ (15) y _M = y _C −p cos θ (16) Moving the viewpoint to a position where the feature point M can be seen from the left and right cameras, that is, the arc ⌒ _{L r} R _{l in} FIG. Moving the viewpoint position upward does not require precise movement control and can be easily performed by the operator's operation. Formula (15), (1
From 6), the angle θ between the measurement coordinates (~ x _C , ~ y _C ) of the cylinder center point C and the measurement coordinates (~ x _M , ~ y _M ) of the feature point M is θ = tan ^-1 {(( ~ x _M) - obtained as _{(~ y C))} (} 17) - (~ x C)) / ((~ y M). However, the range of θ is −90 ° <θ <90 ° because the measurement condition of the characteristic point M, that is, the characteristic point M is visible from the left and right cameras.

As shown in FIG. 3, the coordinates of the viewpoint O ₁ before face-to-face correspondence are represented by x ₁ y ₁ and the coordinates of the viewpoint O ₂ after face-up are represented by x ₂ y _2. First, the viewpoint O ₁ is represented. Consider that the image is rotated by an angle θ, and then t _{X is} translated along the x ₂ axis, which is the x axis after the rotation, to make it face-to-face. In this case, from the geometrical relationship, t
_X becomes t _X = x _C cos θ + y _C sin θ (18). Also, the distance between the viewpoint and the center of the cylinder after facing is x
_{Since C} cos θ-y _C sin θ, the manipulator can be moved from the viewpoint O ₂ to the desired position along the y ₂ axis in a state of being faced based on this information.

FIG. 4 shows the process of face-to-face conversion under the same conditions as in the first embodiment. Here, θ ^{0 is set} to 30 ° and t _X ^{0 is set} to 0.76, and the measurement error is also given to the measurement of the feature point M by a normal random number. Since the initial position is distant from the power pole, the error included in the image plane projection point position measurement affects θ and t _X , but the first moving position is not accurately obtained, but the second and subsequent power poles cannot be obtained. It can be seen that they are correctly faced as they get closer. This is because the stereo image measurement error has the property of being approximately proportional to the square of the measurement distance. According to the present embodiment, since the measurement error of the center point of the cylinder is small, it is possible to more accurately face the center point than in the case of measuring the center point of the cylinder.

In each of the above-mentioned embodiments, the case of two-dimensional measurement is described as an example for simplification, but it goes without saying that it can be extended to the case of three-dimensional measurement.

[0030]

As described above, according to the method for measuring the center position / radius of the cylinder of the present invention, the stereo image is arithmetically processed to detect the cylinder contact surface from the image, and the projection center of the left and right cameras is used to detect the cylinder contact surface. The equation of the four tangents drawn is calculated, and the center of the cylinder is defined as the position where the sum of squares is the minimum between the length of the perpendiculars drawn from the virtual center of the cylinder to each tangent and the average value of these perpendiculars. Since it is a method of calculating and calculating the average value at that time as the radius, it is possible to avoid the systematic error that occurs when applying stereo image measurement to the cylinder center position and radius measurement, and compared to the conventional method There is an advantage that accuracy can be greatly improved.

[Brief description of drawings]

FIG. 1 is a flowchart for explaining a basic embodiment of the present invention.

FIG. 2 is a diagram for explaining a specific first embodiment of the present invention.

FIG. 3 is a diagram for explaining a method of measuring and controlling a viewpoint position.

FIG. 4 is a diagram for explaining a third embodiment when the present invention is applied to viewpoint position measurement control.

FIG. 5 is a diagram for explaining the principle of stereo image measurement.

FIG. 6 is a block diagram of a device configuration for performing stereo image measurement.

FIG. 7 is a diagram for explaining a stereo image measurement model for a cylindrical object.

FIG. 8 is a diagram showing a result of an error when measured by a conventional method.

Claims (1)

[Claims] 1. A method of measuring the center position and radius of a cylindrical object using stereo image processing, the first step of calculating the stereo image to detect the contact surface of the cylinder from the image, and the stereo image. Obtain the equation of n tangent lines drawn from the projected center of the camera to the tangent surface of this cylinder.
And the sum of squares of the difference between the length p _{i of the} perpendicular line drawn from the virtual center of the cylinder to each tangent line based on the equation of the tangent line and the average value ^- p of these perpendicular lines E = Σ _{i = 1} ⁿ (p _i
- ^- p) the length of the perpendicular drawn to the tangent at this time along with the coordinates of the evaluation function E is varied in the virtual center is the center position of the cylinder seeking the coordinate values is minimized ² as an evaluation function And a third step of obtaining an average value of the above as a radius, and a cylinder center position / radius measuring method.