JPH1123241A - Object tilt angle measuring method and apparatus, and storage medium - Google Patents

Abstract

(57) [Summary] [Object] To measure a minute inclination angle with higher accuracy by image processing. A relationship between an area S of a circumscribed rectangle of a binary image of an object, an area S0 of a binary image of the object, and the inclination angle θ with respect to a desired posture of the object is obtained in advance, and the relationship between the area S2 of the object and the inclination angle θ is determined. The areas S and S0 are measured for the value image, and the inclination angle θ is determined based on the relationship. This relationship is substantially defined by the equation S0 =
{XY- (X ² + Y ² ) cos θ sin θ} / {cos
⁴ θ (1-tan ² θ) ² } or an expression S0 approximating this
= XY− (X ² + Y ² ) (sin 2θ) / 2,
Here, X and Y are the lengths of two adjacent sides of the rectangle. The sign of the inclination angle θ is determined based on the coordinates of the four corners of the binary image of the object, or the object 2 existing in one of the predetermined corner-side areas and the other predetermined corner-side area of the end of the circumscribed rectangle. The determination is made based on the difference in the number of pixels of the value image.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for measuring a tilt angle of an object by processing a binary image of the object and a storage medium storing a program for executing the method.

[0002]

2. Description of the Related Art FIG. 6 shows a schematic configuration of a conventional semiconductor chip attitude adjusting device. This device adjusts the attitude of the semiconductor chip 10 while it is being transported by a robot. The hand 11 and the rotary drive device 12 are a part of a transfer robot, and the semiconductor chip 10
The rotation angle of the hand 11 can be adjusted by the rotation driving device 12. The semiconductor chip 10 is imaged by the imaging device 13, and a video signal VS of the image is output from the imaging device 13. The image input circuit 14 generates an address based on the synchronization signal included in the video signal VS, and converts the luminance signal included in the video signal VS into two.
It is converted into a value and written to this address of the image memory 15.
The binary image of the semiconductor chip 10 stored in the image memory 15 is processed by the image processing device 16 and the semiconductor chip 10
Is measured. The rotation angle control circuit 17 rotates the hand 11 through the rotation driving device 12 by −θ in order to set the inclination angle θ to 0 in one operation.

As shown in FIG. 7A, an image processing device 16 raster-scans a binary image 10G in an image memory 15 and performs coordinate (X1, Y1) coordinates of corner points P1 and P2 of the binary image 10G. ) And (X2, Y2). The inclination angle θ is calculated as follows: θ = tan ⁻¹ {(Y2−Y1) / (X1−X2)} (1)

[0004]

However, when the inclination angle θ is small, the candidate for the point P1 is scanned as shown in FIG. 7B due to a quantization error in the binarization in the image input circuit 14. Since a plurality of pixels exist on the line SL1, the measurement accuracy is reduced. In addition, a pixel value inverted to “1” due to noise may be a candidate for the point P1 or the point P2,
Measurement accuracy is further reduced.

[0005] Such a problem also occurs in a pattern inspection apparatus for detecting an inclination defect of an electronic component mounted on a circuit board by image processing or an apparatus for measuring a minute inclination angle of an arbitrary object by image processing. An object of the present invention is to provide an object inclination angle measuring method and apparatus and a storage medium capable of measuring a minute inclination angle with higher accuracy by image processing in view of such a problem.

[0006]

According to a first aspect of the present invention, there is provided an object inclination angle measuring method for processing a binary image of an object to measure an inclination angle θ of the object with respect to a desired posture. The relationship between the area S of the circumscribed rectangle of the binary image, the area S0 of the binary image of the object, and the inclination angle θ is determined in advance, and the area S and the area S of the binary image of the object are determined.
0, and the inclination angle θ is determined based on the relationship.

According to the object tilt angle measuring method, since the tilt angle θ of the object is measured based on the areas S0 and S, the influence of the pixel value inversion due to the quantization error of binarization and noise is small. This has the effect that the inclination angle θ can be measured with higher accuracy than when directly measuring the inclination of a straight line connecting two corner points with respect to the binary image. In the object tilt angle measuring method according to the second aspect, in the first aspect, the binary image of the object is a rectangle, and the relation is substantially expressed by the equation S0 = XY− (X ² + Y ² ) (sin 2θ) / 2. Where X and Y are the lengths of two adjacent sides of the rectangle.

The term “substantially” has a meaning including the case where an equation obtained by modifying this equation is used (the same applies hereinafter). According to this object inclination angle measuring method, there is an effect that the calculation can be simplified and the inclination angle θ can be easily and quickly measured. According to a third aspect of the present invention, in the second aspect, when the area ratio XY / S0 is substantially smaller than the predetermined value, the area ratio XY / S0 is equal to or larger than the predetermined value based on the above equation. In this case, the expression tan θ = (Y2-Y1) / (X1-X2)
Is calculated based on the inclination angle θ.

According to the method for measuring the tilt angle of an object, there is an effect that the calculation is further simplified. According to a fourth aspect of the present invention, there is provided a method for measuring an inclination angle of an object, comprising:
The value image is a rectangle, and the above relationship is substantially equivalent to the equation S0 =
{XY- (X ² + Y ² ) cos θ sin θ} / {cos ⁴
θ (1−tan ² θ) ² }, where X and Y are the lengths of two adjacent sides of the rectangle.

According to this method of measuring the tilt angle of the object, it is possible to obtain the tilt angle θ more accurately than in the case of the second and third aspects. According to a fifth aspect, in any one of the second to fourth aspects, the sign of the inclination angle θ is determined based on the coordinates of two or more points of the binary image of the object. According to this object inclination angle measuring method, it is possible to easily determine whether the inclination angle θ is positive or negative.

According to a sixth aspect of the present invention, in the method of any one of the second to fourth aspects, it is determined whether or not a pixel of the binary image of the object exists in a predetermined area at an end of the circumscribed rectangle. Whether the inclination angle θ is positive or negative is determined based on the inclination angle θ. According to the object tilt angle measuring method, an effect is obtained that the tilt angle positive / negative determination process can be performed in parallel with the calculation of the object pixels to obtain the area S0.

According to a seventh aspect of the present invention, in the object inclination measuring method according to the second aspect, a binary image of the object existing in one of the predetermined corner-side areas and the other predetermined corner-side area of the end of the circumscribed rectangle is provided. The sign of the inclination angle θ is determined based on the difference in the number of pixels. According to this method of measuring the object inclination angle, the effect of the pixel value inversion due to noise is almost eliminated, and even if the inclination angle is minute, the determination result is more accurate than in the case of claim 6.

[0013] In the storage medium of claim 8, claims 1 to 7 are provided.
A program for obtaining the inclination angle θ based on the relationship described in any one of the above is stored. 10. An object inclination angle measuring apparatus for processing a binary image of an object to measure an inclination angle θ of the object with respect to a desired posture, wherein an area S0 of the binary image of the object and a binary image of the object Is measured, and the inclination angle θ is determined based on the relationship between the area S0, the area S, and the inclination angle θ.

[0014]

Embodiments of the present invention will be described below with reference to the drawings. [First Embodiment] FIG. 1 shows an inclination angle measuring procedure according to a first embodiment of the present invention. The process of FIG. 1 is executed by an image processing device, for example, the image processing device 16 of FIG. This image processing apparatus includes, for example, a computer. The numerical values in parentheses below are the step identification numbers in FIG.

(20) As shown in FIG. 2A, the frame image in the image memory 15 is raster-
The coordinates (X1, Y) of the four corner points P1 to P4 of the value image 10G
1) to (X4, Y4) are detected. Points P1 to P4 are from “0” to “1” and “1” when raster scanning is performed.
Corresponding to the extreme values of the X coordinate and the Y coordinate of the point of change from “0” to “0”. These coordinates may be detected from a differential image of the binary image 10G.

(21) The binary image 10G shown in FIG.
The lengths X and Y of the sides of the circumscribed rectangle Q1Q2Q3Q4 are measured. The circumscribed rectangle is a straight line parallel to the X axis through the point P1, a straight line parallel to the Y axis through the point P2, a straight line parallel to the X axis through the point P3, and a straight line parallel to the Y axis through the point P4. It is obtained as a rectangle surrounded by Side length X and Y
Can be measured, so that the circumscribed rectangle Q1Q2Q3Q4
It is not necessary to ask itself. When the inclination angle θ is positive, it is obtained as X = X4-X2, Y = Y3-Y1 (2) as is clear from FIG. When the inclination angle θ is negative, X = X1−X3, Y = Y4−Y2 (3) The following DX and DY are related to Expressions (2) and (3), DX = (X4-X2)-(X1-X3) (4) DY = (Y3-Y1)-(Y4-Y2) (5), DX> 0 and DY> 0 are satisfied when the inclination angle θ is positive, and DX <0 when the inclination angle θ is negative.
DY <0 holds.

One of DX and DY may be used to determine whether the inclination angle θ is positive or negative. However, when the inclination angle θ is a small angle, these are not established due to quantization errors and pixel inversion due to noise. It is possible. Therefore, in order to reduce the influence of pixel inversion due to quantization error or noise, the sign of the inclination angle θ is determined by the sign of D = DX + DY (6), and X is determined by the above (2) or (3). And Y.

(22) The area S0 of the binary image 10G is measured. The area S0 can be easily and accurately obtained by counting the number of “1” pixels in the raster scan in step 20 described above. The reason why the accuracy is good is that positive and negative quantization errors are averaged by the cumulative addition of “1”, and the ratio of noise becomes extremely small.

(23) Ratio S / S0 between area S = XY of circumscribed rectangle Q1Q2Q3Q4 and area S0 of binary image 10G
Increases, the inclination angle θ increases. When the inclination angle θ is large to some extent, the measurement accuracy of the inclination angle θ obtained by the above-described conventional method is relatively high, and the inclination angle θ can be calculated in a short time. Therefore, if XY / S0 ≧ K with respect to a predetermined comparison constant K described later, step 2 is executed.
Go to step 4, otherwise go to step 25.

(24) The inclination angle θ is calculated by the above equation (1), and the inclination angle measurement processing ends. (25-27) If D> 0, the inclination angle θ is calculated by the following approximate expression: θ = 0.5 sin ⁻¹ {2 (XY−S0) / (X ² + Y ² )} (7) Otherwise, it is calculated by the following approximate expression: θ = −0.5 sin ⁻¹ {2 (XY−S0) / (X ² + Y ² )} (8)

The above approximate expression is obtained as follows. X0 = P1P2 = P3P4, ΔX = P1Q1 = P3Q3 (9) Y0 = P2P3 = P4P1, ΔY = P2Q2 = P4Q4 (10) X0 = ΔY / sinθ (11) Y0 = ΔX / sinθ (12) tanθ = ΔY / (X−ΔX) = ΔX / (Y−ΔY) (13) This equation (13) Therefore, ΔX and ΔY are represented by the following equations.

ΔX = tan θ (Y−X tan θ) / (1−tan ² θ) (14) ΔY = tan θ (X−Y tan θ) / (1−tan ² θ) (15) ΔX is calculated by the equations (11) and (12), respectively.
Substituting into X0 = (X−Y tan θ) / cos θ (1-tan ² θ) (16) Y0 = (Y−X tan θ) / cos θ (1-tan ² θ) (17) Expressions (16) and ( 17) In the denominator and numerator on the right side of
Multiplying by θ gives the following equation:

[0023] X0 = (Xcosθ-Ysinθ) / {cos 2 θ (1-tan 2 θ)} · (18) Y0 = (Ycosθ-Xsinθ) / {cos 2 θ (1-tan 2 θ)} · (19 Therefore, the area S0 = X0 · Y0 of the binary image 10G is represented by the following equation.

S0 = (Xcosθ−Ysinθ) (Ycosθ−Xsinθ) / ｛cos^Four θ (1-tan^Twoθ)^Two｛= ｛XY- (X^Two+ Y^Two) Cos θ sin θ｝ / ｛cos^Fourθ (1-tan^Twoθ) ^Two ２０ (20) Here, when the inclination angle θ is sufficiently small, cos^Fourθ ≒ 1, tan^Twoθ ≒ 0 (21) Since Equation (20) can be considered, Equation (20) is approximated as follows:
be able to.

S = XY− (X ² + Y ² ) cos θ sin θ = XY− (X ² + Y ² ) (sin 2θ) / 2 (22) From this equation (22), the above approximate equations (7) and (8) ) Is obtained. The comparison constant K in step 23 is determined in consideration of the degree of noise in the image and how much error the approximation of equation (21) is allowed. The inclination angle θ and the equation (2) of the equation (7)
The relation between 0) and the approximation error is as follows.

When θ = 5 °, COS ⁴ θ (1-tan ²
θ) ² = 0.96984 (about 3.1%) When θ = 10 °, COS ⁴ θ (1-tan ² θ) ² =
0.88303 In (about 11.7%) This first embodiment, based on the area S0 of the binary image 10G and the binary image X ² and Y ² dimensions of the area S = XY and area of a circumscribed rectangle of 10G Since the inclination angle θ of the object is measured, even if the inclination angle θ is small, the effects of the quantization error and noise described in the section of the related art become small, and the inclination angle θ can be measured with higher accuracy. it can. [Second Embodiment] It is also possible to determine whether the object inclination angle θ is positive or negative without using D described above. This will be described below as a second embodiment.

FIGS. 3A to 3C are enlarged top views of the binary image 10G of FIG. 2A. As shown in FIG. 3A, the intersection of a straight line passing through the midpoint C between the points Q1 and Q2 and having a slope of | θ | and a straight line Q2Q3 is defined as R2. | Θ | is
It is obtained from the above equation (7). If the pixel of the binary image 10G does not exist in the triangle CQ2R2, that is, '1'
If the pixel does not exist, it is determined that the inclination angle θ is positive, and if the pixel of “1” exists, it is determined that the inclination angle θ is negative.

FIG. 3B shows another positive / negative determination method.
In this method, the intersection of a straight line passing through the midpoint C between the points Q1 and Q2 and having a slope of − | θ | and a straight line Q1Q4 is defined as R1. If the pixel of '1' exists in the triangle CQ1R1, it is determined that the inclination angle θ is positive, and if the pixel of '1' does not exist, it is determined that the inclination angle θ is negative. FIG. 3C shows another positive / negative determination method. This method uses the above-mentioned two ideas, and uses the triangle CR1Q1
If the difference between the number of “1” pixels existing in the triangle and the number of “1” pixels existing in the triangle CQ2R2 is positive, it is determined that the inclination angle θ is positive. Is determined to be negative. According to this method, the influence of bit inversion due to noise is almost eliminated.

[Third Embodiment] In the first and second embodiments, the case where the binary image is rectangular has been described.
Paying attention to the fact that the ratio of the area S of the circumscribed rectangle of the binary image to the area S0 of the binary image is a function of the object inclination angle θ, it is possible to measure the minute inclination angle θ of an object having an arbitrary shape. It is.

FIG. 4A shows a case where the binary image 10AG is a triangle, and FIG. 4B shows a case where the binary image 10BG is a triangle.
Shows a case where is a bottle shape. Binary image 10A
In the case of G, the relationship between the area ratio S / S0 and the inclination angle θ can be theoretically calculated. In the case of the binary image 10BG, the relationship between the inclination angle θ and the area ratio S / S0 as shown in FIG. 5 is obtained in advance by image processing, and this is tabulated or represented by an approximate expression. When measuring the tilt angle, the area ratio S / S0
Is obtained by image processing, and the inclination angle θ is obtained from the relationship.

In the third embodiment, since the object inclination angle θ is measured based on the area ratio S / S0, even if the inclination angle θ is small, the quantization error and the noise described in the section of the prior art will be reduced. The influence is reduced, and the inclination angle θ can be measured with higher accuracy than when directly measuring the inclination of a straight line connecting the two corners to the binary image. The present invention also includes various modified examples.

For example, instead of using the above approximation formulas (7) and (8), a function f (θ) = ｛XY− (X ² + Y ² ) obtained by subtracting the left side from the right side of the above equation (20) before approximation. cos θ sin θ｝ / {cos ⁴ θ (1−tan ² θ) ² ｝ −S0 (23), and by substituting numerical values for X, Y and S0 on the right side, the equation f (θ) = 0 is satisfied. The solution θ may be obtained by a 探索 search method, a Newton-Raphson method, or the like. In this case, the processing of steps 23 and 24 in FIG. 1 is unnecessary.

The expression for determining whether the inclination angle θ is positive or negative is D
Other than X, DY or D are also conceivable. For example, the inclination angle θ
Is positive, X4> X1, X3> X2, Y2> Y1, and Y3> Y4 are satisfied. When the inclination angle θ is negative, the relations in which these inequality signs are reversed are satisfied. Alternatively, the sign of the inclination angle θ may be determined by the sign, such as X4-X1 + Y2-Y1 or (X4-X1) / X + (Y2-Y1) / Y.

FIG. 3 is used to determine whether the inclination angle θ is positive or negative.
The inner region is not limited to a triangle. For example, in FIG. 3C, when the midpoint of the straight line R1R2 is D, a rectangle D
The number of '1' pixels present in CQ1R1 and the rectangle DC
If the difference from the number of “1” pixels existing in Q2R2 is positive, it is determined that the inclination angle θ is positive, and if not, the inclination angle θ
May be determined to be negative. In this case, the points R1 and R
The position of 2 may be any position as long as it is equidistant from points Q1 and Q2.

[Brief description of the drawings]

FIG. 1 is a flowchart showing a procedure for measuring an object inclination angle according to a first embodiment of the present invention.

FIG. 2 is an explanatory diagram of an object inclination angle measuring method used in the processing of FIG. 1;

FIG. 3 is an explanatory diagram of an object inclination angle positive / negative determination method according to a second embodiment of the present invention.

FIG. 4 is an explanatory view of an object inclination angle measuring method according to a third embodiment of the present invention.

FIG. 5 is a diagram showing a relationship between an inclination angle of an object and an area ratio.

FIG. 6 is a schematic configuration diagram of a conventional semiconductor chip attitude adjusting device.

FIG. 7 is an explanatory view of a conventional method of measuring an object inclination angle.

[Explanation of symbols]

 Reference Signs List 10 semiconductor chip 10G, 10AG, 10BG binary image 11 hand 12 rotation drive device 13 imaging device 14 image input circuit 15 image memory 16 image processing device 17 rotation angle control circuit SL1 to SL4 scan line θ tilt angle

Continuing from the front page (72) Inventor Akihiko Yabuki 4-1-1, Kamiodanaka, Nakahara-ku, Kawasaki-shi, Kanagawa Prefecture Inside Fujitsu Limited (72) Inventor Hitoshi Komoriya 4-1-1, Kamiodanaka, Nakahara-ku, Kawasaki-shi, Kanagawa Prefecture Inside Fujitsu Limited (72) Inventor Tetsuo Hitsuka 4-1-1 Kamikadanaka, Nakahara-ku, Kawasaki City, Kanagawa Prefecture Inside Fujitsu Limited

Claims (9)

[Claims] 1. An object inclination angle measuring method for processing a binary image of an object to measure an inclination angle θ of the object with respect to a desired posture, comprising: an area S of a circumscribed rectangle of the binary image of the object; The relationship between the area S0 of the binary image and the inclination angle θ is determined in advance, the area S and the area S0 are measured for the binary image of the object, and the inclination angle θ is determined based on the relationship. An object inclination angle measuring method, characterized in that: 2. The binary image of the object is rectangular, and the relationship is substantially determined by the equation S0 = XY− (X ² + Y ² ) (s
2. The method according to claim 1, wherein X and Y are lengths of two adjacent sides of the rectangle. 3. When the area ratio XY / S0 is substantially smaller than a predetermined value, the area ratio XY / S0 is calculated based on the above equation.
If S0 is equal to or greater than a predetermined value, the expression tan θ = (Y2-Y
3) The method for measuring an object inclination angle according to claim 2, wherein the inclination angle θ is calculated based on 1) / (X1−X2). 4. The binary image of the object is rectangular, and the relationship is substantially determined by the equation S0 = ｛XY- (X ² + Y ² ) co
The object according to claim 1, wherein sθ sin θ｝ / {cos ⁴ θ (1-tan ² θ) ² }, wherein X and Y are the lengths of two adjacent sides of the rectangle. Tilt measurement method. 5. The method according to claim 2, wherein the sign of the inclination angle θ is determined based on the coordinates of two or more corners of the binary image of the object. Object tilt angle measurement method. 6. The method according to claim 2, wherein the positive or negative of the inclination angle θ is determined based on whether or not a pixel of the binary image of the object exists in a predetermined region at an end of the circumscribed rectangle. The method for measuring an inclination angle of an object according to any one of the above. 7. A method for determining whether the inclination angle θ is positive or negative based on a difference in the number of pixels of a binary image of the object existing on one corner side predetermined area and the other corner side predetermined area of the end of the circumscribed rectangle. The method according to claim 2, wherein the determination is performed. 8. A storage medium storing a program for obtaining the inclination angle θ based on the relationship according to claim 1. Description: 9. An object inclination angle measuring apparatus for processing a binary image of an object to measure an inclination angle θ of the object with respect to a desired posture, the area S0 of the binary image of the object and the binary image of the object Measuring the area S of the circumscribed rectangle of the object and obtaining the inclination angle θ based on the relationship between the area S0, the area S, and the inclination angle θ.