JPH02210206A - Center indexing method for circle - Google Patents

Abstract

PURPOSE:To take a highly accurate measurement even with low resolution by finding the coordinates of intersections of (n) scanning lines parallel to an X and a Y axis and arcs, every semicircle, and calculating the center coordinates of the circle from specific expressions when the center of the circle is indexed by image processing on X-Y orthogonal coordinates. CONSTITUTION:When the center of the circle is indexed by the image processing on the X-Y orthogonal coordinates, the coordinates of intersections of (n) scanning lines parallel to the X axis and the arcs and the coordinates of intersections of (n) scanning lines parallel to the Y axis and the arcs are found, every semicircle. Then the center coordinates of the circle are calculated from the expressions to take a highly accurate measurement even with the low resolution.

Description

TECHNICAL FIELD OF THE INVENTION The present invention relates to a method for determining the center of a circle by image processing.

BACKGROUND ART As a method for accurately measuring the center of a circle in the field of image processing, there is the following measurement method.

The first measurement method, as shown in Figure 5, is to recognize the end of the arc in the moving direction of the arrow through image processing, and then count the amount of rotation of the stepping motor at that time with a rotary encoder to determine the feed pitch. This is a method of finding the center from the radius R of the circle, with the accuracy as follows.

As shown in Figure 6, the second measurement method is to measure the entire circle with high resolution n in the X and Y directions within the frame.
This is a technique that recognizes divided scanning lines, counts the number of scanning lines outside the diameter in each direction, and calculates the center coordinates.

Furthermore, as shown in Figure 7, the third measurement method is to determine the recognition position of the camera in advance, recognize the arc at the four ends of the circle, and use the number of dots to determine the number of dots in the X-axis and Y-axis directions. This is a technique of counting the diameter from the number of dots divided into n division pitches.

All of these techniques have an accuracy of 1 due to the camera resolution.
Furthermore, since only arcs on one or two diameters of the circle are observed, accurate data for the entire circle cannot be obtained,
As a result, the accuracy of the measurement data decreased, making it difficult to accurately determine the center.

OBJECTS OF THE INVENTION Accordingly, it is an object of the present invention to obtain data for an entire circle and accurately determine the center of a circle in the field of image processing.

Solution to the Invention Based on the above object, the present invention obtains coordinates at four points on a circle in each of the X and Y directions, and averages the center of the circle based on the four coordinates.

1 and 2 illustrate the principle of the invention. First, in Figure 1, on the X-Y orthogonal coordinates, the center coordinates of the circle are
It is obtained from the following equation by averaging the intersection coordinates x, , Xz between the axis and the circular arc, and the intersection coordinates yl, yz between the Y axis and the circular arc, respectively.

Since this technique is basically the same as the technique of FIGS. 6 and 7 already described, there is a limit to its measurement accuracy.

Next, Fig. 2 shows the 4th axis of the circle in the
Intersection coordinates XI, xz, X2, Xa, yl,
y2, y3, and y4 are obtained, and the center coordinates of the circle are obtained by averaging them. That is, the center coordinates of each circle are determined by the following formulas.

According to this measurement principle, the intersection coordinates are found at eight points on the circle, and these values are averaged, so even with low resolution,
The center coordinates of a circle can be measured with high accuracy.

The center determining method of the present invention is based on the above principle,
The above measurement principle is extended to each characteristic of the field of image processing, that is, the number of scanning lines, and the measurement is performed with low resolution and high precision while grasping the entire circle of the measurement target.

Measuring device configuration FIG. 3 shows the configuration of the measuring device 1.

A circle 2 such as an optical disk to be measured is placed within the movement range of the camera 3. Then, this camera 3 is moved by the X-Y positioning device 4 to the measuring position of the circle 2 on the optical disk, observes the circle 2 there, and stores it in the frame memory 5.

The image processing device 6 has a built-in program based on the center determining method of the present invention, and based on commands from the keyboard 7, the data of the circle 2 from the frame memory 5 and the amount of movement of the X-Y positioning device 4 are stored. Based on the data, etc., necessary calculations are performed to determine the center of the circle 2, and the center is displayed on the display 8 or recorded on the printer 9 (.

Method for determining the center of a circle During measurement, the X-Y positioning device 4 sequentially moves each X-axis and Y-axis to respective measurement points on the X-Y orthogonal coordinates. The data on the amount of movement at this time is input to the image processing device 6.

Of course, there is no need to move the camera 3 when all of the measuring points of the circle are captured in the field of view.

Here, the field of view of the camera 3 is, for example, 58.5(n), and the number of dots in the X-axis and Y-axis directions is 512, respectively.
．． It is 480. Therefore, the accuracy in the X-axis and Y-axis directions is as follows.

X-axis direction accuracy: 585001512 = 114.3
(μn/dat) Y-axis direction accuracy: 58500/480
= 121.9 (,lJm/dat) Next, the camera 3 images the arc using n scanning lines parallel to the X axis at each of the four measurement points, that is, the upper and lower semicircles, and It is converted into an electrical signal and stored in the frame memory 5. Therefore, the image processing device 6 uses image processing to find the intersection between each scanning line and the circular arc, finds the coordinates of the intersection on the X axis from the number of dots, and calculates the X coordinate of the center of the circle 2 from the number 2 below. do.

Similarly, the camera 3 images the arc using n scanning lines parallel to the Y-axis at each of the four measurement points, that is, the left and right semicircles, converts the image into an electrical signal, and stores it in the frame memory. 5 to be memorized. Therefore, the image processing device 6 determines the intersection of each scanning line and the circular arc by image processing,
The coordinates of the intersection on the Y axis are determined from the number of dots, and the Y coordinate of the center of circle 2 is calculated from the following formula.

According to this measurement, 0 measurements are performed at a total of 8 intersection coordinate positions, and the average is calculated, so even if the scanning line and number of dots have low resolution, the intersection coordinate value is This can be determined with high precision by averaging over the entire circle.

Although this method was developed on the premise of fixing the hub at the center position of an optical disk, it can also be used in other center locating fields, such as locating the center of a nozzle hole, locating the center of an IC flat package, or locating the center of a processing object. This can be applied when moving a circular workpiece to the origin of a coordinate system.

Effects of the Invention In the present invention, four intersection coordinates are observed for each of the X-axis and Y-axis directions on the circumference, and n intersection coordinates are determined for each intersection coordinate, and these are averaged. This makes it possible to measure with high accuracy even with low resolution, and since the entire circumference is observed, the reliability is higher than data from partial observation positions.

[Brief explanation of the drawing]

Figures 1 and 2 are explanatory diagrams of the measurement principle of the present invention;
The figure is a block diagram of the measuring device, FIG. 4 is an explanatory diagram of the measurement situation, and FIGS. 5, 6, and 7 are explanatory diagrams of the conventional measuring method. 1. Measuring device, 2. Circle of optical disk, etc., 3. Camera, 4. X-Y positioning device, 5. Frame memory, 6. Image processing device, 7. Keyboard, 8. Display. , 9...Printer. Figure 7 Figure 3 Figure 4

Claims (1)

[Claims] When determining the center of a circle on the X-Y orthogonal coordinates by image processing, the intersection coordinates of n scanning lines parallel to the X axis and the circular arc for each semicircle, and A method for determining the center of a circle, characterized in that the coordinates of the intersections of n scanning lines parallel to the Y-axis and the circular arc are determined, and the coordinates of the center of the circle are calculated from the following arithmetic expression. ▲There are mathematical formulas, chemical formulas, tables, etc.▼ ▲There are mathematical formulas, chemical formulas, tables, etc.▼