JPH0644399A - Method for measuring center position of circle - Google Patents

Abstract

PURPOSE:To obtain the center position and radius of the circle with high accuracy by measuring the center of the circle with respect to a set of respective edge points divided into sections and deciding the center of the circle by majority. CONSTITUTION:The edge point is detected from two-dimensional picture data and the set of the edge points is divided into sections. In the concrete, the center of gravity 6 of the edge point is calculated to divide 360 deg. into M pieces. The section division is performed at boundaries 7 of the section division of an edge point string 5 according to the M-divided angle centering the center of gravity 6. The circular arc approximation is performed by the mean quadruplicate error minimization method with respect to the set of edge points in each section to estimate the position of the center of the circle and radius, and to calculate the area where horizontal positions of the center of the circle, vertical positions of the center of the circle, and radii are most densely concentrated. Further, the position of the center of the circle and radius is decided by taking the mean of positions of the center of the circle and radii in the section where the horizontal positions of the center of the circle, the vertical positions of the center of the circle, and the radii are most densely concentrated. Thus, the position and radius of the circular arc can be obtained with high accuracy eliminating the adverse effects such as dusts and missing from the picture data.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a circle center position measuring method used when measuring and inspecting shapes of products and parts using image data.

[0002]

2. Description of the Related Art A conventional method for detecting an arc from image data will be described.

The conventional method for detecting a circular arc consists of the following three steps.

Edge points are extracted from the two-dimensional image data.

A point sequence is created from edge points.

An arc is approximated from a sequence of points.

First, the step of extracting edge points from the two-dimensional image data will be described.

An edge point is a point at which the image density changes abruptly. Since the absolute value of the differential is large at such a point, the point where the absolute value of the output is large can be used as the edge point by performing image filtering with the differential filter. An example of the differential filter is a Laplacian filter as shown in FIG. Further, in order to obtain a point sequence edge point, it is sufficient to extract a ridge as shown in FIG. 2 for the differential value of the image data, and therefore, for the 8 neighboring points as shown in FIG. Those that satisfy two or more conditions are regarded as edge points.

X ≧ X ₀ and X> X ₄ X ≧ X ₁ and X> X ₅ X ≧ X ₂ and X> X ₆ X ≧ X ₃ and X> X ₇ Next, a point sequence is created from the edge points of The steps will be described.

In order to obtain a necessary point sequence from the set of edge points obtained in step 3, adjacent edge points are connected. At this time, the point sequence may be branched, but short branches are removed, and for long branches, only the point sequence having the smallest curvature is left, and the other points are disconnected so that the point sequence has no branching. .

Here, the curvature is calculated as follows. Figure 4
Branch point P shown in (the point branching from here)
And the points apart from P by a certain length L are Q ₁ and Q ₂ , and the ratio of θ = π− (angle Q ₁ −P−Q ₂ ) and L

[0012]

[Equation 1]

Let be the curvature.

The value of L is determined to be smaller than the radius of the circumference to be detected. However, if it is too small, it becomes sensitive to noise.

The point sequence obtained as described above is set as {P _i | i = 1 ... N}.

Next, the step of approximating a circular arc from the point sequence by the mean square error minimization method will be described.

The mean square error minimization method will be described below.

[0018]

[Equation 2]

[Mathematical formula-see original document] is a circle equation, which can be rewritten as follows.

[0020]

[Equation 3]

For any point (x, y), the square of the distance from the arc center (a, b) to the point (x, y) is the left side of (2) (x-a) ² + (y-b) ) Equal to ² .

The left side of equation (2) minus the right side is (3)
Since it is equal to the left side of the equation, the left side of equation (3) can be said to be the “difference between the square of the distance from the arc center (a, b) to the point (x, y) and the square of the arc radius r”.

Here, the evaluation value E is defined as follows.

[0024]

[Equation 4]

However, f (x, y) is a differential value at the point (x, y).

E is the sum of weights obtained by weighting the differential values at each squared point in equation (3). A, B, which minimizes E
If C is obtained, a circle approximating a given set of edge points can be obtained.

Therefore,

[0028]

[Equation 5]

[0029]

[Equation 6]

[0030]

[Equation 7]

As equation (5), (6) and (7), the simultaneous equations may be solved. The solution is as follows.

[0032]

[Equation 8]

[0033]

[Equation 9]

[0034]

[Equation 10]

However,

[0036]

[Equation 11]

V () indicates variance, C () indicates covariance, and bar indicates average.

That is,

[0039]

[Equation 12]

[0040]

[Equation 13]

[0041]

[Equation 14]

[0042]

[Equation 15]

[0043]

[Equation 16]

[0044]

[Equation 17]

[0045]

[Equation 18]

[0046]

[Formula 19]

However,

[0048]

[Equation 20]

The center coordinates (a, b) of the circle and the radius r are A,
It can be calculated from B and C as follows.

[0050]

[Equation 21]

[0051]

[Equation 22]

[0052]

[Equation 23]

With this, the position and radius of the arc can be obtained from the image.

By the above processing, the position and radius of the arc can be approximated from the two-dimensional image.

[0055]

However, in the above conventional method, as shown in FIG. 5, when the circle to be recognized is a hole, the edge of the hole is a perfect circle due to chipping of the edge of the hole or dust. There is a problem in that, when it is distorted, the error in the position and radius of the measured circle may be large due to the edge of the chip or the dust.

In view of the above conventional problems, it is an object of the present invention to provide a circle center position measuring method that does not increase the error even when the edge is distorted from a perfect circle due to chipping or dust.

[0057]

A circle center position measuring method of the present invention comprises a step of detecting edge points from two-dimensional image data, a step of dividing a set of edge points into sections, and an edge point in each section. A step of estimating a circle center position and radius by performing an arc approximation by a mean square error minimization method for a set of, and a step of calculating the most densely gathered area for the estimated circle center position and radius, It is characterized by comprising the step of determining the circle center position and the radius by taking the average of the circle center position and the radius in the region.

[0058]

According to the present invention, after the edge points are detected from the two-dimensional image data by the above-mentioned structure, the set of edge points is divided into sections, and the center of the circle is measured for each set of the divided edge points to obtain the circle points. Since the circle center is decided by the majority vote of the circle center for each section, the circle center of the section affected by chips or dust will be excluded to find the circle center.
Measurement errors due to chips and dust can be removed.

[0059]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A circle center position measuring method according to an embodiment of the present invention will be described below with reference to FIGS.

FIG. 5 is a diagram of a hole whose position is to be measured. 1 is a hole, 2 is a circumference of an edge of the hole, 3 is dust attached to the edge of the hole, and 4 is a chip of the edge of the hole. .

With respect to such a hole, the center position of the hole is measured from the two-dimensional data by the following steps.

Edge points are detected from the two-dimensional image data. As the edge point detection method, the same method as the conventional example is used. FIG. 6 shows edge points detected in the image data of the hole 1 shown in FIG. 5, and 5 is an edge point sequence.

The set of edge points is divided into sections. Specifically, the center of gravity of the edge point is calculated, 360 degrees is divided into M, and the section is divided according to the angle obtained by dividing the center of gravity by M. The number of divisions M is determined in the following way.
The average size of dust and chip size is S, and the radius of a circle is d (if it is known in advance, it is used, and if not known, the average value of the distance between the center of gravity of edge points and each edge point is used. ),

[0064]

[Equation 24]

(Total circumference 2π is divided by estimated angle S / d). In FIG. 6, 6 is the center of gravity of the edge point sequence,
Reference numeral 7 is a boundary of section division when M = 4.

An arc approximation is performed on the set of edge points in each section by the method of minimizing the mean square error, and the position and radius of the circle center are estimated. The mean square error minimization method is the same method as the conventional example. FIG. 7 shows the result of circle approximation for each section according to the section division shown in FIG. 8
Is the estimated circle center in each section.

An area in which the horizontal position of the circle center, the vertical position of the circle center, and the radius are most densely gathered is calculated. Specifically, as shown in FIG. 8, the screen is divided by a grid 9 and the partition in which the estimated circle centers are most concentrated is searched for in the partition divided by the grid. If the edge point sequence section division number M is small and there is no difference in the number, it may be supplemented by adding the number of adjacent 4 sections or 8 sections for each section.

The position / radius of the center of the circle is defined as the average of the positions / radius of the center of the circle in the section where the horizontal position of the center of the circle, the vertical position of the center of the circle, and the radii are most closely packed. Also in this case, if the edge point sequence section division number M is small and there is no difference in number, the adjacent four sections or eight sections may be added together for each section and the circle center position / radius may be averaged.

With this, it is possible to remove the adverse effects of the dust 3 and the chip 4 from the image data and obtain the position and radius of the arc with high accuracy.

[0070]

According to the present invention, after the edge points are detected from the two-dimensional image data as described above, the set of edge points is divided into sections, and the center of the circle is measured for each set of the divided edge points. However, since the center of the circle is determined by majority, even if there is a chip or dust, the influence of those can be removed, and the center position and radius of the circle can be obtained with high accuracy.

[Brief description of drawings]

FIG. 1 is an explanatory diagram of a Laplacian filter for differentiating image data.

FIG. 2 is an explanatory diagram of ridge extraction for obtaining edge points as a point sequence.

FIG. 3 is used to set a condition to be regarded as an edge point 8
It is explanatory drawing of a neighboring point.

FIG. 4 is an explanatory diagram of curvature calculation when cutting a point sequence.

FIG. 5 is a diagram of holes to be measured in one embodiment of the present invention.

FIG. 6 is an explanatory diagram of section division of edge points.

FIG. 7 is a circle approximation diagram for each edge point section.

FIG. 8 is a grid division diagram of a screen for determining a circle center by majority decision.

[Explanation of symbols]

 1 hole 2 hole edge 3 dust on hole edge 4 hole edge missing 5 edge point sequence 6 center of gravity of edge point 7 boundary of section division of edge point sequence 8 estimated circle center for each section

Claims (1)

[Claims] 1. A step of detecting edge points from two-dimensional image data, a step of dividing a set of edge points into sections, and an arc approximation by a mean square error minimization method for a set of edge points in each section. Performing a step of estimating the position and radius of the circle center, a step of calculating the most densely gathered area for the estimated circle center position and radius, and the circle center position with the average of the circle center position and radius within this area. And a circle center position measuring method.