JP3608771B2 - Rotation angle detection method, apparatus and recording medium - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a rotation angle detection method and apparatus for detecting a rotation angle of a specific pattern from an image, and a recording medium on which a rotation angle detection program is recorded.
[0002]
[Prior art]
The present applicant has previously proposed a rotation angle detection method for accurately detecting the rotation angle of a pattern image using the characteristics of Zernike moment (Japanese Patent Application No. 10-4224). The method proposed in the previous application will be described below.
[0003]
FIG. 6 shows the configuration of the embodiment of the above application. FIG. 7 is a process flowchart of the embodiment of the above application. A pattern (for example, FIGS. 13 and 14) is input to the image input unit 11. Then, when such a pattern is input, its center coordinate is given and the pattern image is normalized (step 201). Although the input image is a binary image, when the input image is a color image, the brightness is obtained and the binary image is created and used by comparing the brightness with a predetermined threshold value.
[0004]
The product-sum operation unit 12 aligns the center coordinates of the pattern image with the center of the Zernike polynomial table 13 (step 202). After alignment, the product sum of each pixel value of the pattern image and the corresponding value in the table is calculated to calculate Zernike moment (hereinafter referred to as ZM) (step 203).
[0005]
Here, a product-sum calculation is performed on the pattern image and three types of Zernike polynomial tables (hereinafter referred to as ZPT) 13 prepared in advance. 8, 9, and 10 show examples of ZPT. In these figures, white pixels have a value of −63 and black pixels have a value of 63 (halftone gray (a peripheral color portion) has a value of 0). The center of the circle is the ZPT center coordinate (0, 0), the X axis is positive on the right side, and the Y axis is positive on the upper side.
[0006]
FIG. 8 shows the third-order first-floor ZPT. (A) is the real part, and (b) is the imaginary part having a rotational relationship of π / 2. The floor represents the number of cycles on the circumference. Since the number of cycles on the first floor is 1 (white to black), it is hereinafter referred to as ZPT of cycle 1.
[0007]
FIG. 9 shows the fourth-order second-order ZPT (ZPT with a period number of 2 and a period of 2 hereinafter), (a) is the real part thereof, and (b) is the imaginary part having a rotational relation of π / 4. is there.
[0008]
FIG. 10 shows the sixth-order fourth-order ZPT (ZPT with a period number of 4 and a period of 4 hereinafter), (a) is the real part thereof, and (b) is the imaginary part having a rotational relationship of π / 8. is there.
[0009]
FIG. 11 shows an example in which the real part 33 of ZM is obtained by multiplying the ZPT (here, the real part table) 31 and the corresponding pixel value of the image 32.
[0010]
That is, since the input image is a binary image, the sum of the pixel values of ZPT corresponding to the black pixels of the input image is calculated. As described above, since the ZPT of this embodiment is composed of three types of tables with periods 1, 2, and 4, the summation process is as follows.
Real part ZPT with period 1 and imaginary part ZPT with period 1
Real part ZPT with period number 2 and imaginary part ZPT with period number 2
Real part ZPT with period number 4 and imaginary part ZPT with period number 4
A total of 6 ZMs are calculated (steps 203 and 204). In the above example, cycles 1, 2, and 4 are processed in order, but these can also be processed in parallel. Further, the number of periods is not limited to the above, and other number of periods may be used. Furthermore, although the above-described example is an example of a binary image, a multi-valued image can be processed similarly.
[0011]
After that
Zmr1 represents the real part ZM obtained from the ZPT having the cycle number 1, Zmi1 represents the imaginary part ZM obtained from the ZPT having the cycle number 1,
Zmr2 represents the real part ZM obtained from the ZPT having the cycle number 2, Zmi2 represents the imaginary part ZM obtained from the ZPT having the cycle number 2,
Zmr4 represents the real part ZM obtained from the ZPT having the cycle number 4, Zmi4 represents the imaginary part ZM obtained from the ZPT having the cycle number 4,
It expresses.
[0012]
The ZM calculation unit 14 calculates the size of the ZM defined by the following formula for each cycle (step 205). The size of each ZM is a rotation invariant value.
[0013]
ZM magnitude Zmag1 = [Zmr1] ² + [Zmi1] ² obtained from the ZPT having a period of 1
ZM magnitude Zmag2 = [Zmr2] ² + [Zmi2] ² obtained from ZPT having a period of ²
ZM magnitude Zmag4 = [Zmr4] ² + [Zmi4] ² obtained from the ZPT with a period of 4
Next, the ZM determination unit 15 determines the validity of the ZM size by collating it with the ZM size of the pattern registered in the dictionary 16.
[0014]
That is, when the predetermined threshold values are Th1 and Th2, Zmag1 in cycle 1 is Th2 <Zmag1 <Th1.
Whether or not (step 206),
Similarly for cycle 2, when the predetermined thresholds are Th3 and Th4, Zmag2 of cycle 2 is Th4 <Zmag2 <Th3.
(Step 207),
Similarly for cycle 4, when the predetermined threshold values are Th5 and Th6, Zmag4 of cycle 4 is Th6 <Zmag4 <Th5.
(Step 208), the following process is executed only when all of Zmag1, Zmag2, and Zmag4 satisfy the above-described conditions, and otherwise the process is terminated.
[0015]
Next, the evaluation value calculation unit 17 calculates an evaluation value for each period (step 209). Here, the evaluation value is expressed as (ZM size) × number of periods (floor). For example, the evaluation value for cycle 1 is Zmag1 × number of cycles (floor = 1).
[0016]
The rotation angle calculation unit 18 calculates the rotation angle θ1 from the real part Zmr1 (or imaginary part Zmi1) of period 1, calculates the rotation angle θ2 from the real part Zmr2 (or imaginary part Zmi2) of period 2, and A rotation angle θ4 is calculated from the real part Zmr4 (or imaginary part Zmi4) (step 210).
[0017]
Hereinafter, calculation of the rotation angle in each cycle (floor) will be described.
Calculation of rotation angle in period 1 (floor 1);
If the period is 1, the rotation angle is uniquely determined between 0 and 2π based on the Zernike moment calculated from the input image (if the input image is periodic in the circumferential direction, Although the rotation angle corresponding to the number of cycles of the image is obtained, the same image is obtained when the image is corrected based on the rotation angle regardless of which rotation angle is used in the processing after the rotation angle calculation).
[0018]
In order to calculate the rotation angle with high accuracy, the smaller the absolute value of the real part Zmr1 or the imaginary part Zmi1 of period 1 (the change rate of the real part Zmr1 and the change rate of the imaginary part Zmi1 with respect to the change of the rotation angle) Calculate using the larger one). When calculating the rotation angle, the relationship between the rotation angle and Zernike moment is used.
[0019]
FIG. 12 is a diagram showing the relationship between the rotation angle and the Zernike moment, where (a) is the third and first floor, (b) is the fourth and second floor, and (c) is the sixth and fourth floor. Indicates. The rotation angle on the horizontal axis is obtained by quantizing one round (2π) to 296, and the vertical axis is the real part of the Zernike moment (the imaginary part of the Zernike moment (not shown) is π / 2 is out of phase). This figure collects the calculated values of the real part of ZM when 360 degrees is divided into 360 equal parts and the dictionary creation image is rotated by 1 degree (1 degree, 2 degrees, 3 degrees ... 360 degrees) (Table). Therefore, the rotation angle of the input image can be obtained by referring to the table using the real part obtained from the product sum of an input image and ZPT.
[0020]
In addition to this, as a calculation method of the rotation angle, since tan φ = imaginary part of ZM / real part of ZM, φ = arctan (imaginary part of ZM / real part of ZM), φ = arcsin (imaginary number of ZM) Part / ZM size).
[0021]
The specific procedure is as follows.
(1) A Zernike moment (real part Zmr1, imaginary part Zmi1) is calculated from the input image.
(2) A Zernike moment with a small absolute value is selected from the real part Zmr1 and the imaginary part Zmi1.
(3) Data having the closest value among the Zernike moments selected for each rotation angle is detected, and the rotation angle at that time is set as the rotation angle of the input image. For example, in (a), when the value closest to the real part of the selected Zernike moment is Re1, the rotation angle is θ1.
[0022]
Calculation of the rotation angle in period 2 (floor 2);
When the period is 2, two rotation angle candidates are obtained between 0 and 2π based on the Zernike moment calculated from the input image. Of the two, one is the correct rotation angle, but one has the Zernike moment periodicity and does not accurately represent the image rotation angle.
[0023]
Therefore, the process for calculating the rotation angle is performed in the same manner as in the case of the period 1 described above between 0 and π. A rotation angle calculated between 0 and π and an angle obtained by adding π to the rotation angle are candidates for the rotation angle in period 2.
[0024]
When the input image has a specific pattern and no error, the rotation angle calculated in cycle 1 is equal to the rotation angle calculated in cycle 2. Here, assuming that the error is small (less than π / 2), the rotation angle of cycle 2 is the one closer to the rotation angle of cycle 1 among the two rotation angle candidates obtained in cycle 2. In the example of FIG. 12B, θ2 close to θ1 is the rotation angle in period 2.
[0025]
Calculation of rotation angle in period 4 (floor 4);
Similarly to the case of the period 2, when the period is 4, four rotation angle candidates are obtained between 0 and 2π. In period 4, the rotation angle is obtained between 0 and π / 2 in the same manner as in the case of period 1 described above, and this rotation angle and the angle obtained by adding π / 2, π, and 3π / 2 to this rotation angle are set to four. Candidate for rotation angle.
[0026]
When the rotation angle is selected from the four rotation angle candidates, the rotation angle of the cycle 4 is obtained with reference to the rotation angle of the cycle 1 or the cycle 2 assuming that the error is relatively small.
[0027]
In order to determine the rotation angle to be referred to (one from the rotation angle of cycle 1 and the rotation angle of cycle 2), the above-described evaluation value is used. When the evaluation value for cycle 1 is larger than the evaluation value for cycle 2, the rotation angle closest to the rotation angle of cycle 1 among the four rotation angles obtained in cycle 4 is set as the rotation angle of cycle 4. Similarly, when the evaluation value for cycle 2 is larger than the evaluation value for cycle 1, the rotation angle of cycle 4 is the one closest to the rotation angle of cycle 2. The rotation angles of the periods 1, 2, and 4 calculated in this way are defined as θ1, θ2, and θ4.
[0028]
Subsequently, the rotation angle selection unit 19 selects a rotation angle having the largest evaluation value among the three evaluation values calculated in Step 209 (Step 211).
[0029]
The angle difference determination unit 20 has a difference between the rotation angles θ1 and θ2 as θa, a difference between θ2 and θ4 as θb, and a difference between θ1 and θ4 as θc.
θa + 2θb + 2θc <Th (predetermined threshold)
Is satisfied (step 212). When the above condition is satisfied, the rotation angle output unit 21 outputs the rotation angle selected at step 211 (step 213). Otherwise, the process ends.
[0030]
[Problems to be solved by the invention]
In the above-described application, as shown in FIGS. 12A to 12C, when calculating the rotation angle using the Zernike moment having the period number 2, the two rotations obtained from the Zernike moment having the period number 2 are used. In order to select the correct rotation angle from the angle (circled number 2), it was necessary to refer to the rotation angle calculated from the Zernike moment with a period number of 1.
[0031]
Similarly, when calculating the rotation angle using the Zernike moment with the cycle number 4, the correct rotation angle is selected from the four rotation angles (circled number 3) obtained from the Zernike moment with the cycle number 4. Therefore, it is necessary to refer to the rotation angle calculated from the Zernike moments of the cycle number 1 and the cycle number 2. As described above, the proposed method requires a large amount of processing to accurately detect the rotation angle.
[0032]
The present invention improves the proposed invention,
An object of the present invention is to provide a rotation angle detection method, apparatus, and recording medium that detect a rotation angle with a smaller amount of processing.
[0033]
[Means for Solving the Problems]
In order to achieve the above object, according to the first aspect of the present invention, there is provided a rotation angle detection method for detecting a rotation angle of a pattern image in an image using a Zernike moment of an order / rank from which a plurality of rotation angles are calculated. Then, a set of coordinates calculated at a specific position in the pattern image without being influenced by rotation in the pattern image is calculated as a feature value, and the feature value is used to calculate the Zernike moment. One rotation angle is selected from a plurality of rotation angles.
[0034]
The invention according to claim 2 is characterized in that the center of the pattern image is used as coordinates calculated at a specific position in the pattern image.
[0035]
The invention according to claim 3 is characterized in that the center of gravity of the pattern image is used as coordinates calculated at a specific position in the pattern image.
[0036]
The invention according to claim 4 uses a set of coordinates calculated at a specific position in the pattern image without being influenced by rotation in the pattern image, and when the distance between the coordinates is short, the Zernike moment with a small rank is used. When a single rotation angle is selected with reference to the rotation angle calculated from the above and the distance between the coordinates is far, a plurality of Zernike moments having a large number of ranks are calculated using the feature amount according to claim 1 . One rotation angle is selected from the rotation angles.
[0037]
In the invention according to claim 5, when means for inputting a pattern image, means for calculating a plurality of Zernike moments having different orders and ranks of the pattern image, and Zernike moments having a rank of 2 or more are used. Means for calculating a plurality of rotation angles based on Zernike moments, means for calculating a set of coordinates calculated at a specific position in the pattern image without being influenced by rotation in the pattern image, and Means for selecting one rotation angle from the plurality of rotation angles using the feature amount, and means for outputting the selected rotation angle as a rotation angle of the inputted pattern image. It is said.
[0038]
According to a sixth aspect of the present invention, there is provided means for inputting a pattern image, means for calculating a plurality of Zernike moments having different orders and ranks of the pattern image, and information including the Zernike moment rank to be used for the specific pattern. And means for calculating a plurality of rotation angles based on the Zernike moment of the rank in the storage means, and is calculated at a specific position in the pattern image without being affected by the rotation in the pattern image. Means for calculating a set of coordinates as a feature amount, means for selecting one rotation angle from the plurality of rotation angles using the feature amount, and the selected rotation angle of the input pattern image Means for outputting as a rotation angle, and a first component part comprising the storage means and a second component part comprising other means excluding the storage means Release, is characterized in that the said first component and second component are connected via a network.
[0039]
In the invention according to claim 7, when a function for inputting a pattern image, a function for calculating a plurality of Zernike moments having different orders and ranks of the pattern image, and a Zernike moment having a rank of 2 or more are used. A function for calculating a plurality of rotation angles based on Zernike moment, a function for calculating a set of coordinates calculated as a specific position in the pattern image without being affected by the rotation in the pattern image , A function for causing a computer to realize a function of selecting one rotation angle from the plurality of rotation angles and a function of outputting the selected rotation angle as a rotation angle of the input pattern image using the feature amount It is a computer-readable recording medium on which a program is recorded.
[0040]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, an embodiment of the present invention will be described in detail with reference to the drawings.
Example 1
In the present invention, when calculating the rotation angle using the Zernike moment with the period number 2 or the period number 4, when selecting the correct rotation angle from a plurality of calculated rotation angles, it is calculated from the Zernike moment with a smaller period number. Instead of referring to the rotation angle, a method that can calculate the rotation angle at a high speed with lighter processing than the method using Zernike moment is used to reduce processing.
[0041]
FIG. 1 shows the configuration of Embodiment 1 of the present invention. In the figure, an image input unit 1, a product-sum operation unit 2, a Zernike polynomial table 3, a Zernike / moment calculation unit 4, a Zernike / moment determination unit 5, a dictionary 6, and a rotation angle output unit 9 are the same as those in the application described above. It is.
[0042]
In the present invention, the rotation angle calculation unit of the previous application is replaced with a first rotation angle calculation unit 7 and a second rotation angle calculation unit 8 is provided.
[0043]
FIG. 2 is a processing flowchart of the first embodiment of the present invention. The processing up to step 108 is the same as the processing up to step 208 in the processing flowchart of the above-mentioned application. The second rotation angle calculation unit 8 calculates a rotation angle based on the positional relationship between the center and the center of gravity of the input pattern image (step 109), and the first rotation angle calculation unit 7 calculates the rotation calculated in step 109. Using the angle, the rotation angle calculated from the Zernike moment is selected, and the rotation angle is obtained with higher accuracy (step 110). In other words, when using Zernike moments with a period of 2 or more, for which multiple rotation angles are calculated, the positional relationship between the center and the center of gravity (that is, the pattern image is not affected by rotation and specified in the pattern image). The rotation angle calculated from the Zernike moment that is closest to the rotation angle calculated from the set of coordinates calculated at the position of (3) is selected and output as the rotation angle of the pattern image.
[0044]
A method for obtaining the rotation angle from the positional relationship between the center of the input pattern image and the center of gravity will be described with reference to FIG. The center of gravity (Xg, Yg) can be calculated using the following equation.
Xg = Σxf (x, y) / Σf (x, y)
Yg = Σyf (x, y) / Σf (x, y)
In FIG. 3, an angle formed by a line segment between the X axis and the center of gravity at the rotation angle 0 is α. Here, in the input pattern image, if the angle formed by the line segment between the X axis and the center of gravity is β, the rotation angle of the input pattern image can be obtained by β−α.
[0045]
Although the rotation angle calculated from the center and the center of gravity is easy to process, the accuracy is often low. Therefore, in the present invention, the rotation angle is calculated in combination with the technique of the above-mentioned application.
[0046]
4A to 4C are the same as those described with reference to FIGS. 12A to 12C. In FIG. 4, for example, when calculating the rotation angle using the cycle number 4, the rotation angle closest to β−α (θ4) is used instead of referring to the rotation angles of the cycle numbers 1 and 2 as in the above-mentioned application. ) Is selected. By using this method of the present invention, conventionally, when the rotation angle is calculated using the Zernike moment with a period number of 4, it has been necessary to refer to the rotation angle with the period number of 1 or 2. Even when the Zernike moment is used, the rotation angle can be calculated with high accuracy from a plurality of rotation angles calculated from one Zernike moment.
[0047]
In the above example, the number of periods 4 is used, but the same applies to the case of periods 2 and it is not necessary to refer to the rotation angle of period 1. Further, whether to use the number of periods 2 or 4 is performed as follows, for example. When the input pattern image is a specific pattern, it is recorded in advance in the dictionary 6 that, for example, a Zernike moment having a period of 4 is used, and the ZM determination unit 5 acquires this information when determining the Zernike moment. The first rotation angle calculation unit 7 may be passed. The first rotation angle calculation unit 7 calculates only a rotation angle with a period number of 4 ((c) in FIG. 4). If the use of Zernike moments with a period of 1 is recorded in the dictionary 6, θ1 is output in the same manner as in the previous application (FIG. 4A).
[0048]
In the above-described embodiment, the center of gravity is used as the most typical example. However, as long as the coordinates of the same point are always calculated on the pattern image without being affected by the rotation of the pattern image, Coordinates may be used. For example, the following coordinates may be used.
Xh = Σx ² f (x, y) / Σf (x, y)
Yh = Σy ² f (x, y) / Σf (x, y)
In any case, it is preferable that the coordinates calculated by the center of gravity or a specific method (which is always calculated at a specific position in the mark) and the center position are separated by a predetermined threshold or more.
[0049]
When this distance is close (below a predetermined threshold value), a method of referring to the rotation angle calculated from the Zernike moment with a small number of cycles is used together as in the past. In other words, the conventional method is used for pattern images where the distance between the center and the center of gravity is close, and for pattern images where the distance between the center and the center of gravity is far away, the rotation number calculated from the center and the center of gravity is used. Select a rotation angle calculated from many Zernike moments.
[0050]
As described above, for example, in a detection system for marks or the like, a plurality of marks are often to be detected. Therefore, the speed of the entire system can be increased by using the method of the present invention even in some processes.
[0051]
1, the dictionary 6 may be provided on the server side, the other components may be provided on the client side, and the client side and the dictionary may be connected via a network. When such a configuration is adopted, the latest information such as a dictionary can always be used.
[0052]
(Example 2)
The present invention is not limited to the above-described embodiments, and can be realized by software. When the present invention is realized by software, as shown in FIG. 5, a computer system including a CPU, a memory, a display device, a hard disk, a keyboard, a CD-ROM drive, a scanner, etc. is prepared, and a computer such as a CD-ROM is prepared. A program that realizes the rotation angle detection function of the present invention is recorded on the readable recording medium, and this program is installed in the system. An image input from an image input unit such as a scanner is temporarily stored in a hard disk or the like. When the program is started, the temporarily stored image data is read, a rotation angle detection process is executed, and the detection result is output to a display or the like. Since the pattern image to be detected may change due to various factors, a method of operating the system using the latest information at all times by accessing a part of information such as a dictionary via the network. take.
[0053]
【The invention's effect】
As described above, according to the present invention, when the rotation angle of a pattern image in an image is detected using a Zernike moment with a cycle number of 2 or more in which a plurality of rotation angles are calculated, Since the rotation angle calculated from the center of gravity is referred to, it is not necessary to refer to a rotation angle with a smaller number of cycles, and the processing is speeded up.
[Brief description of the drawings]
FIG. 1 shows a configuration of Embodiment 1 of the present invention.
FIG. 2 is a process flowchart of Embodiment 1 of the present invention.
FIG. 3 is a diagram for obtaining a rotation angle from the center and the center of gravity of an input pattern.
4A to 4C are diagrams illustrating selection of a rotation angle. FIG.
FIG. 5 shows a configuration of Embodiment 2 of the present invention.
FIG. 6 shows a configuration of an embodiment of the prior invention.
FIG. 7 shows a processing flowchart of an embodiment of the invention of the prior application.
FIGS. 8A and 8B show the third-order first-order ZPT.
FIGS. 9A and 9B show the fourth-order second-order ZPT.
FIGS. 10A and 10B show sixth-order fourth-floor ZPTs.
FIG. 11 shows an example in which ZM is obtained by multiplying ZPT and a corresponding pixel value of an image.
FIG. 12 is a diagram showing a relationship between a rotation angle and Zernike moment.
FIG. 13 shows an example pattern.
14 shows an example in which the pattern of FIG. 13 is rotating.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 Image input part 2 Sum-of-products calculation part 3 Zernike polynomial table 4 ZM calculation part 5 ZM determination part 6 Dictionary 7 1st rotation angle calculation part 8 2nd rotation angle calculation part 9 Rotation angle output part

Claims (7)

A rotation angle detection method for detecting a rotation angle of a pattern image in an image using an order / rank Zernike moment for which a plurality of rotation angles are calculated, wherein the pattern image is not affected by rotation in the pattern image. A set of coordinates calculated at a specific position in the inside is calculated as a feature amount, and one rotation angle is selected from a plurality of rotation angles calculated by the Zernike moment using the feature amount. Rotation angle detection method. Rotation angle detecting method according to claim 1, characterized by using the center of the pattern image as coordinates calculated to a particular position in the pattern image. Rotation angle detecting method according to claim 1, characterized by using the center of gravity of the pattern image as coordinates calculated to a particular position in the pattern image. Use a set of coordinates calculated at a specific position in the pattern image without being affected by rotation in the pattern image, and refer to the rotation angle calculated from the Zernike moment with a small rank when the distance between the coordinates is short Then, when one rotation angle is selected and the distance between the coordinates is far, one rotation angle is calculated from a plurality of rotation angles calculated by the Zernike moment having a large number of ranks using the feature amount according to claim 1. A method of detecting a rotation angle, comprising: selecting. Means for inputting a pattern image, means for calculating a plurality of Zernike moments having different orders and ranks of the pattern image, and a plurality of Zernike moments having a rank of two or more. Means for calculating a rotation angle, means for calculating a set of coordinates calculated at a specific position in the pattern image without being influenced by rotation in the pattern image , and using the feature amount, A rotation angle detection apparatus comprising: means for selecting one rotation angle from a plurality of rotation angles; and means for outputting the selected rotation angle as the rotation angle of the input pattern image. Means for inputting a pattern image; means for calculating a plurality of Zernike moments having different orders and ranks of the pattern image; means for storing information including the Zernike moments to be used for a specific pattern; and the storage A feature set is a means for calculating a plurality of rotation angles based on the Zernike moment of the rank in the means and a coordinate set calculated at a specific position in the pattern image without being affected by the rotation in the pattern image. Means for calculating, means for selecting one rotation angle from the plurality of rotation angles using the feature quantity, and means for outputting the selected rotation angle as a rotation angle of the input pattern image. A first component comprising the storage means and a second component comprising other means excluding the storage means, the first component When the rotation angle detecting device is characterized in that the second component are connected via a network. A function of inputting a pattern image, a function of calculating a plurality of Zernike moments having different orders and ranks of the pattern image, and a Zernike moment having a rank of 2 or more, a plurality of Zernike moments are used based on the Zernike moments. A function of calculating a rotation angle, a function of calculating a set of coordinates calculated at a specific position in the pattern image without being influenced by rotation in the pattern image , and using the feature amount, A computer-readable recording medium storing a program for causing a computer to select a rotation angle from a plurality of rotation angles and a function to output the selected rotation angle as a rotation angle of the input pattern image. recoding media.

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