JPH10269364A - Method for processing image of mobile object, its device and recording medium for recording program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To process the image of an object in a random arrayal by preventing the output of data of the image which is discriminated to be the same object as the last time image by means of a same object discriminating processing and outputting data of the image except it. SOLUTION: A robot controller 41 judges the position and the posture of the object on a conveyor 3 by an output signal from an image processor 1 and controls a robot 4 so as to execute work. The feature value of the inputted image which is picked-up by a camera is extracted and the mobile quantity of the image corresponding to the object by the movement of the object from the input of the last time image to the input of the this time image, that is, an image mobile quantity is obtained. The image inputted this time is compared with the last time one so as to execute the same object discriminating processing for discriminating the image by the object being the same as the one corresponding to the last time image from the this time images by considering the image mobile quantity. Data of the image which is discriminated to be the same as the last time image by the discriminating processing is not outputted and data of the image except it is outputted.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an image processing method and apparatus for a moving object which captures an image of the object conveyed in a fixed direction by a conveyor or the like and outputs the data to an external device such as a robot controller. It is about.

[0002]

2. Description of the Related Art When an object such as a part or a product is conveyed by a conveyor or the like and automatically assembled or packed by a robot or the like, a means for detecting the position of the object corresponding to the eyes of the robot is required. Become. As the position detecting means,
An image of an object is captured by an image input device such as a video camera, the image is analyzed, and data such as the shape and position of the object is sent to a robot controller or the like to control the robot. The timing of image input is determined by a trigger signal that commands image input to the image input device. Conventionally, as a trigger signal, the fact that an object has entered the visual field of a screen is detected by a light detection element, a microswitch, or the like, and the detection signal is used.

[0003]

In the conventional image processing apparatus, the trigger signal for instructing the timing of image input is generated by the object detecting device. It required complicated and cumbersome work. In addition, the detection of an object can be reliably performed only when the objects are conveyed in a row at substantially equal intervals, the objects are randomly distributed, and also in the width direction of the conveyor. When there are a plurality of objects, it is difficult to output a detection signal for detecting that the object has entered the visual field of view corresponding to each object. It is also difficult to associate each detection signal with an image of each object. Therefore, it was not possible to perform image processing on a random array of objects using a conventional image processing apparatus.

Accordingly, the present invention provides an image processing method for a moving object, which can perform image processing of an object without requiring a device for detecting the object, and can perform image processing of an object having a random arrangement. And an apparatus.

[0005]

In order to achieve the above object, a moving object image processing method according to the present invention captures an image of a moving object in a fixed direction within a visual field of a screen and outputs the data. An image processing method, wherein an image of the entire screen visual field is input at a time interval shorter than the time when an object passes through the screen visual field and stored in the storage means, and the previously input image is also stored in the storage means. In advance, the feature value of the input image is extracted, and the movement amount of the image corresponding to the target object due to the movement of the target object between the input of the previous image and the input of the current image, that is, the image movement amount is calculated. Calculate and compare the currently input image with the previous image, and determine the image of the same object as the object corresponding to the previous image from the current image in consideration of the image movement amount. Perform the discrimination process and Data of an image is determined to be the same object and the previous image by the object discriminating process does not output, is obtained so as to output the data of the other image.

In the image processing method for a moving object, the same object discriminating process includes, as a search start position, a position obtained by moving a previous image by a predetermined amount from the image moving amount. The images present in the moving direction from the search start position and having the same characteristic value can be regarded as the same object.

In the above-mentioned moving object image processing method, the same object discriminating processing includes the step of moving the previous image by the image moving amount within a predetermined range. Can be determined to be the same object.

Further, the image processing apparatus for a moving object according to the present invention is an image processing apparatus for capturing an image of an object moving in a fixed direction within a visual field of a screen and outputting the data.
Image input signal generating means for generating an image input signal for inputting an image of the entire screen visual field at a time interval shorter than the time when the object passes through the screen visual field, and image storing means for storing the input image A previous image storage means for storing the previously input image, a feature value extracting means for extracting a feature value of the input image, and a target object between the input of the previous image and the input of the current image. Image moving amount obtaining means for obtaining the moving amount of the image corresponding to the target object by moving, that is, the image moving amount, comparing the image input this time with the previous image, and considering the image moving amount, The same object discriminating means for discriminating an image of the same object as the object corresponding to the previous image from the images, and the same object as the previous image is discriminated by the same object discriminating means. Image de Data is not output, and an image information output means for outputting the data of the other image.

In the moving object image processing apparatus, the same object discriminating means may use a position obtained by subtracting a previous image by a predetermined amount from the image moving amount as a search start position. In this case, it is possible to use an image which is present in the moving direction from the search start position and has the same feature value as the current image as the same object.

In the image processing apparatus for a moving object, the same object discriminating means may be located within a predetermined range from a position at which a previous image has been moved by the image moving amount, and Can be used if the images of this time that match are the same object.

Further, the recording medium in which the image processing program for a moving object of the present invention is recorded is provided on a computer for capturing an image of the object moving in a fixed direction within the visual field of the screen and outputting the data. A step of inputting an image of the entire screen view at a time interval shorter than a time when the image passes through the screen view and storing the image in the storage means, a procedure of storing the image in another area of the storage means, A procedure for extracting the feature value of, and a procedure for calculating the moving amount of the image corresponding to the target object due to the moving of the target object between the input of the previous image and the input of the current image, that is, the image moving amount, The same object discriminating process of comparing an image inputted this time with a previous image and discriminating an image of the same object as the object corresponding to the previous image from the current image in consideration of the image movement amount. Row A program for executing a procedure and a procedure of outputting data of other images without outputting data of an image determined to be the same target as the previous image by the same target object determination process. It is recorded.

However, the term "match" in the present invention does not mean exact matching of numerical values, but means matching within a predetermined range in consideration of errors and the like.

[0013]

Embodiments of the present invention will be described with reference to the drawings. FIG. 1 shows a configuration of an image processing apparatus for a moving object according to the present invention. As the image processing apparatus 1, a small computer such as a so-called personal computer can be used. The image processing apparatus 1 includes a CPU 1 such as a microprocessor as information processing means for performing various data processing.
0, and a ROM 12 and a RAM 13 are connected to the CPU 10 via a bus 11 as main storage devices. The CPU 10 operates according to the system programs and data stored in the ROM 12 and the programs and data loaded in the RAM 13. RAM
The image processing program 133, which will be described later, is an example of the program loaded into the memory 13. Furthermore, the RAM 13
Image memory 131 for storing the data of the image input this time
And an area of the previous image memory 132 for storing the data of the previously input image.

A fixed disk device 14 is connected to the CPU 10 via a bus 11 as an auxiliary storage device. The CPU 10 is transferred from the fixed disk device 14 to the RAM 13.
A program to be executed is loaded.
Further, the CPU 10 is connected to the input / output device 1 via a bus 11.
5 is connected. The input / output device 15 includes an input / output device for an external storage medium such as a flexible disk, a magneto-optical disk, and a CD-ROM. From an external storage medium inserted into the input / output device 15,
The program can be read into the AM 13 or the fixed disk device 14 or, conversely, the programs or data in the RAM 13 or the fixed disk device 14 can be stored in an external storage medium.

A display means 16 for displaying characters and graphics via a bus 11 and an interface circuit to the CPU 10 and an input means 17 for an operator to input data.
Is connected. CRT, EL as display means 16
A display panel, a liquid crystal display panel (liquid crystal display) or the like can be used, and a keyboard or the like can be used as the input means 17. Further, a timer 18 is connected to the bus 11.
The CPU 10 can read time information from the timer 18 and perform processing at regular time intervals or perform processing at a predetermined time.

The bus 11 is connected to a trigger generation circuit 19 for generating a trigger signal for capturing an image with the camera 2. The trigger generation circuit 19 has a CP
Controlled by U10, a trigger signal can be generated under arbitrary conditions, such as generating a trigger signal at fixed time intervals or generating a trigger signal according to the moving distance of the conveyor 3. The camera 2 captures an image of a moving object on the conveyor 3 by a trigger signal. The captured image data is input by the CPU 10 via an interface circuit and stored in the image memory 131.

The conveyor 3 is a conveyor such as a belt conveyor or a roller conveyor, and conveys an object such as a part or a product in a certain direction. From the conveyor 3, a signal indicating the transport distance is input to the image processing apparatus 1, and the CPU 10 can know the transport distance of the conveyor 3, that is, the moving distance of the object. However, it is not essential to input a signal indicating the transport distance from the conveyor 3 to the image processing apparatus 1. Since the speed of the conveyor 3 is substantially constant, the speed of the conveyor 3 is input as a constant, or the object being transported is photographed at predetermined time intervals, and the conveyor 3 is determined based on the amount of movement of the image.
May be calculated.

The robot controller 41 receives the output signal from the image processing apparatus 1 and determines the position of the object on the conveyor 3
The posture and the like are determined, and the robot 4 is controlled to perform an assembling work, a packing work, and the like of the target object.

FIG. 2 is a diagram showing image data taken by the camera 2 and stored in the image memory 131. The image data is displayed in orthogonal coordinates by orthogonal X and Y axes.
The image data has 512 pixels in each of the X-axis direction and the Y-axis direction, and the position is represented by a coordinate value having the origin at the upper left corner of the image. That is, the upper left corner of the image is (X, Y) = (0, 0), and the lower right corner of the image is (5, 5).
11, 511). The image in FIG. 2 includes an image P of a pentagonal object. Here, the mounting position of the camera 2 is set so that the moving direction of the target object is in the X-axis direction. However, it is not essential that the moving direction be the X-axis direction, and the moving direction may be the Y-axis direction or the oblique direction.

The image processing program 133 generates an image P
Are extracted, and then the position of the center of gravity of the image P is calculated and displayed inside the image P, and the image memory 13
1 is also stored. The image processing program 133 extracts various characteristic values of the image other than the center of gravity, if necessary. If the image is a polygon, the position of each vertex is extracted, and if the image is a circle, feature values such as a radius are extracted. Here, in order to simplify the description, it is assumed that only the position of the center of gravity is extracted as the feature value. Information on the characteristic values of the image P is output to the robot control device 41 via the interface circuit. Then, the image data stored in the image memory 131 is copied and stored in the image memory 132 last time.

Thereafter, when a predetermined time elapses or the conveyor 3 moves by a predetermined transport distance, a trigger signal is output to the camera 2 again, and the image data of FIG. 3 is captured. The time interval between the trigger signals is set shorter than the time during which the object passes through the visual field of the screen so that images of all the objects on the conveyor 3 can be captured. When the trigger signal is generated based on the transport distance of the conveyor 3, the trigger signal is generated for each transport distance shorter than the transport distance corresponding to the length of the screen visual field in the X-axis direction.

When the image data of FIG. 3 is stored in the image memory 131 and the characteristic value of the image N included in the image data is extracted, the image data is compared with the previously fetched image data in the previous image memory 132. This image N is an image obtained by moving the object of the previously captured image P, and represents the same object as the previous image data. For such an image, the image data was previously stored in the robot controller 41.
And need not be output again. Outputting again will confuse the control of the robot. Therefore, the image data captured twice or more for the same object is checked and is not output to the robot controller 41.

The amount of movement on the screen from the image P to the image N, that is, the amount of image movement D, is caused by the movement of the conveyor between the previous trigger signal and the present trigger signal. The relationship between the value and the transport distance,
And, it can be calculated by the transport distance of the conveyor 3. Further, the transport distance of the conveyor 3 can be obtained by a signal indicating the transport distance from the conveyor 3 or a time interval between the transport speed of the conveyor 3 and the trigger signal.

At the time of initial setting of the image processing apparatus 1, an object is conveyed by the conveyor 3, and images are taken in at predetermined time intervals as shown in FIGS. The quantity D can be measured directly. The measurement of the image movement amount D may be automatically performed by the image processing apparatus 1, or may be measured on a screen and input by the input unit 16. Image movement amount D
Is proportional to the transport distance of the conveyor 3 or the time interval between the trigger signals, so that their proportional constants are calculated and RA
If it is stored in M13, the image movement amount D can be easily calculated.

FIG. 4 is a view showing an example of a captured image when a plurality of objects are randomly arranged and conveyed on the conveyor 3. The object is represented by circular images P1 to P4. The points inside represent the centers of gravity of the images P1 to P4.
FIG. 5 is a diagram showing the contents of image data stored in the image memory 131. The image memory 131 indicates the image number assigned to each image corresponding to each object, the position of the center of gravity of the image, and indicates that the image is the second or later captured image of the same object. The same flag is stored. If necessary, information on characteristic values other than the position of the center of gravity may be stored.

The image data of the image numbers 1 to 4 corresponds to the image P1
~ P4. Here, since the images P1 to P3 are new images, the same flag of the image data is not turned on, and the image data of the images P1 to P3 is output to the robot control device 41. The same flag is turned on for the image data of the image P4, and the image data of the image P4 is not output. Before output, the image data of the image numbers 1 to 4 is stored in the previous image memory 132 as new previous image data.

FIG. 6 is a view showing a captured image when a plurality of objects in FIG. 4 have moved. Images N1 and N2 are
It is an image of a new object not displayed in FIG.
The images N3 to N5 correspond to the same object as the objects indicated by the images P1 to P3 in FIG. Image movement amount D
Is D = 209, and the images N3 to N5 are images obtained by moving the images P1 to P3 in FIG. 4 by 209 pixels in the X-axis direction. The image N6 is an image obtained by moving the image P4 by 209 pixels. However, since the entire image N6 is not within the field of view of the screen, the image N6 is not assigned an image number and has a characteristic such as a position of the center of gravity. The values and the like are not stored in the image memory 131. In this manner, an image that does not entirely fall within the screen visual field is not stored in the image memory 131.

FIG. 7 is a diagram showing the contents of the image data stored in the image memory 131. Image data of image numbers 1 to 5 correspond to images N1 to N5. Image N1
The contour of N5 is extracted, the position of the center of gravity is calculated, and stored as image data. Here, each image data is compared with the previous image data stored in the previous image memory 132 as shown in FIG. 5, and the same flag is turned on for the image data that has been moved the previous image data by the image movement amount D. . That is, the images N3 to N5 change the images P1 to P3 by the image movement amount D.
, The same flag is turned on.

FIG. 8 is a flowchart showing the processing contents of the image processing program 133. In the judgment 101, the CPU 10 reads the data of the timer 18 and judges whether or not a predetermined time set in advance has elapsed from the previous trigger signal. If the time has not elapsed, the process proceeds to decision 102, where it is determined whether a trigger request is received from an external device such as the robot controller 41 or the like. If there is a trigger request, the process proceeds to step 103; Judgment 101 and Judgment 10
In short, 2 means that the set time elapses from the previous trigger signal or the processing proceeds to processing 103 in response to a trigger request from an external device, and otherwise repeats the loop.

In the process 103, the CPU 10
Is reset, and the trigger generation circuit 19 is controlled to generate a trigger signal for the camera 2. The camera 2 captures an image according to the trigger signal, and starts transmitting the image to the image processing apparatus 1. In processing 104, the CPU 10 inputs image data transmitted from the camera 2 via the interface circuit, and
31. Next, in process 105, the image memory 131
Is analyzed, the contour of the image corresponding to the object is extracted, and the feature value of the image of each object is extracted. The feature value includes the position of the center of gravity, but other feature values may be extracted.

The calling process 106 calls a subroutine for performing the same object discriminating process for setting the same flag. The processing content of the same object determination subroutine will be described in detail in the description of FIG. Next, processing 10
7, the image data in the image memory 131 is stored in the previous image memory 132 as new previous image data. Next, in a process 108, the image data in which the same flag is not turned on from the image data in the image memory 131 is output to an external device such as the robot controller 41. Processing 10
When 8 is completed, the process returns to the determination 101, and the above processing is repeated.

FIG. 9 is a flowchart showing the contents of the same object discriminating subroutine called in the calling process 106. Here, variables representing the positions of the respective centers of gravity of the previous image data are Xp and Yp. That is, (Xp, Yp)
Are coordinates representing the center of gravity. Further, variables representing the barycentric position of the current image data are represented by Xn and Yn, and variables representing coordinate values are represented by X and Y. First, in process 201, the variable X
The barycentric position of the image number 1 from the previous image data in the previous image memory 132 is substituted for p and Yp. For example, image number 1 in FIG. 5 corresponds to image P1 in FIG.

Next, in process 202, variables X and Y are
A value is substituted according to the equation (X = Xp + D−d) and the equation (Y = Yp). Here, D is the image movement amount described above,
d is a predetermined subtraction amount indicating the position at which the search of the image is started. The subtraction amount d is set to several pixels to several tens of pixels in consideration of an error in the conveyor speed of the conveyor 3, an error in time measurement, and the like. The current image of the same object as the previous image at the center of gravity position (Xp, Yp) is searched from the position (X + 1) in the positive direction of the X axis. If the current image of the same object is found by the search, the same flag of the image data is turned on.

In the process 203, 1 is added to the value of the variable X. Next, in judgment 204, an image at the position of the center of gravity (Xn, Yn) that matches the position of the center of gravity (X, Y) obtained from the image data in the image memory 131 by the calculation formula is searched, and such an image exists. Judge whether or not. The determination that the position of the center of gravity (X, Y) matches the position of the center of gravity (Xn, Yn) depends on the linearity of the trajectory of the conveyor 3, the transport speed error,
In consideration of the time error of the timer 18, a width of about several pixels is provided. That is, even if there is a difference of about several pixels between them, it is determined that they match. As described above, the term “match” in the present invention does not mean exact matching of numerical values, but means matching within a predetermined range in consideration of an error or the like.

If there is an image at the position of the center of gravity (Xn, Yn) which coincides with the position of the center of gravity (X, Y), the flow advances to step 205 to turn on the same flag of the image data. If there is no matching image, proceed to decision 206. In the judgment 206, it is judged whether or not the value of the variable X exceeds the maximum value 511 of the X coordinate of the screen. If the variable X exceeds 511, the process proceeds to step 207, and if not, the process returns to step 203 to continue the search for the position of the center of gravity (Xp, Yp). Process 205
And a process 207 next to the judgment 206 terminates the search for the current center of gravity position (Xp, Yp) and sets the variables Xp, Y
The position of the center of gravity of the image following the previous image data is set to p. Then, in the judgment 208, it is judged whether or not there is data of the next center of gravity. If there is, the process returns to the step 202 to start searching for the next position of the center of gravity (Xp, Yp). To return to the caller.

The image processing program 133 performs the above processing. A search start position is defined as a position which is before the position where the previous image is moved by the image movement amount D by the subtraction amount d,
An image of the same object which is present in the moving direction from the search start position and has the same feature value is searched. In this embodiment, only the Y-coordinate of the center of gravity is considered as the feature value, but the coincidence of other feature values may be used as the condition for the same determination. In addition to such a search method, a search may be made for a current image that is near a predetermined range of a position where the previous image has been moved by the image movement amount D and has the same characteristic value. When only the position of the center of gravity is considered as the feature value, the nearest one in the vicinity of the predetermined range may be set as the same object.

In this embodiment, the same object discriminating process is performed in the image processing apparatus 1. However, all image data is output from the image processing apparatus 1 to the robot controller 41, and the same object discriminating processing is performed. Processing is robot controller 4
1 may be performed. In that case, the data of the same object is not output in the output stage from the robot controller 41 to the robot 4. Although the object moves in the X-axis direction of the screen, if the moving direction is the Y-axis direction or the oblique direction, appropriate coordinate conversion (rotation of the coordinate axis, etc.) is performed to change the moving direction to the X-axis direction. After the conversion into the direction, the processing as described in this embodiment may be performed.

[0038]

Since the present invention is configured as described above, it has the following effects.

An object detection device for generating a trigger signal for instructing the timing of image input is not required.
Since complicated and troublesome work requiring skill such as installation work and adjustment work of the detection device is not required, the cost for image processing is reduced.

Even when the objects are randomly distributed and a plurality of objects exist in the width direction of the conveyor, it is possible to output image data corresponding to each object. Further, since image data is output only once for the same target, control of a robot or the like using the output image data is simplified.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating a configuration of an image processing apparatus according to the present invention.

FIG. 2 is a diagram illustrating an example of a captured image;

FIG. 3 is a diagram illustrating an image of a moving target object.

FIG. 4 is a diagram illustrating an example of captured images of a plurality of objects;

FIG. 5 is a diagram illustrating the contents of image data.

FIG. 6 is a diagram illustrating images of a plurality of moved objects.

FIG. 7 is a diagram illustrating the contents of image data;

FIG. 8 is a flowchart illustrating processing contents of an image processing program.

FIG. 9 is a flowchart illustrating a process of determining the same object;

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 ... Image processing apparatus 2 ... Camera 3 ... Conveyor 4 ... Robot 10 ... CPU 11 ... Bus 12 ... ROM 13 ... RAM 14 ... Fixed disk device 15 ... Input / output device 16 ... Display means 17 ... Input means 18 ... Timer 19 ... Trigger Generation circuit 41: Robot controller

Claims (7)

[Claims] An image processing method for capturing an image of an object moving in a fixed direction within a screen visual field and outputting the data, wherein the screen is displayed at a time interval shorter than a time when the object passes through the screen visual field. An image of the entire field of view is input and stored in the storage means (131), and the previously input image is also stored in the storage means (132).
The feature value of the input image is extracted, and the movement amount of the image corresponding to the target object due to the movement of the target object between the previous image input and the current image input, that is, the image The moving amount is obtained, the image input this time is compared with the previous image, and an image based on the same object as the object corresponding to the previous image is determined from the current image in consideration of the moving amount of the image. The same object discriminating process (106) is performed. The data of the image determined to be the same object as the previous image by the same object discriminating process (106) is not output, and the data of the other images is not output. An image processing method for a moving object to be output. 2. The image processing method for a moving object according to claim 1, wherein the same object discriminating process (106) moves the previous image by an amount obtained by subtracting a predetermined amount from the image moving amount. An image processing method for a moving object, in which the searched position is set as a search start position, and the current image existing in the movement direction from the search start position and having the same characteristic value is regarded as the same object. 3. The image processing method for a moving object according to claim 1, wherein the same object discriminating processing (106) is performed within a predetermined range from a position at which a previous image is moved by the image moving amount. Image processing method for a moving object, in which the current image which is in the vicinity of and within which the feature values match is assumed to be the same object. 4. An image processing apparatus for capturing an image of an object moving in a fixed direction in a screen visual field and outputting the data, wherein the screen is displayed at a time interval shorter than a time when the object passes through the screen visual field. Image input signal generation means (19) for generating an image input signal for inputting an image of the entire field of view, and image storage means (131) for storing the input image.
And a previous image storage means (1) for storing a previously input image.
32) and a feature value extracting means (10) for extracting feature values of the input image.
5) and an image moving amount obtaining means (202) for obtaining a moving amount of an image corresponding to the target object due to the moving of the target object between the previous image input and the present image input, that is, an image moving amount. And comparing the image input this time with the previous image, and determining an image based on the same object as the object corresponding to the previous image from the current image in consideration of the image movement amount. Discriminating means (106); image information for not outputting data of an image determined to be the same object as the previous image by the same object discriminating means (106), but outputting data of other images An image processing apparatus for a moving object, comprising: an output unit (108). 5. The image processing apparatus for a moving object according to claim 4, wherein the same object discriminating means (106) moves the previous image by an amount obtained by subtracting a predetermined amount from the image moving amount. An image processing apparatus for a moving object, wherein the position thus set is set as a search starting position, and the current image existing in the moving direction from the search starting position and having the same feature value as the same object. 6. An image processing apparatus for a moving object according to claim 4, wherein said same object discriminating means (106) is a predetermined range from a position at which a previous image has been moved by said image moving amount. An image processing apparatus for a moving object, in which the current image having the same characteristic value and being in the vicinity of the object is regarded as the same object. 7. A computer for capturing an image of an object moving in a fixed direction in a screen visual field and outputting data of the image, wherein the computer reads the image of the object at a time interval shorter than the time when the object passes through the screen visual field. (101-104) for inputting the image of the image and storing it in the storage means, and (10) for storing the image in another area of the storage means.
7), a step (105) of extracting the feature value of the input image, and the movement of the image corresponding to the object due to the movement of the object between the previous image input and the current image input. The procedure of obtaining the amount, that is, the image movement amount (202), comparing the image input this time with the previous image, and taking into account the image movement amount, the current image is the same as the object corresponding to the previous image. The same object discriminating process (106) for discriminating an image based on the object, and the data of the image determined to be the same object as the previous image by the same object discriminating process (106) are output. Procedure for outputting data of other images without performing (108)
Recording medium on which a program for executing the above is recorded.