JP2011203148A - Estimation device, estimation method and estimation program - Google Patents

Abstract

An object of the present invention is to provide an estimation apparatus, an estimation method, and an estimation program capable of estimating an object coordinate system indicating a three-dimensional position / attitude of an object with high accuracy.
An estimation apparatus according to an aspect of the present invention is an estimation apparatus that estimates an object coordinate system that indicates a three-dimensional position / posture of a target object in a space, and is based on an object image obtained by imaging the target object. In order to calculate a plurality of marker coordinate systems corresponding to a plurality of markers detected by the marker detection unit 3, and a marker detection unit 3 that detects a marker that is provided on the target object and can estimate a three-dimensional position / posture by itself. A marker coordinate system estimation unit that estimates a marker coordinate system from each marker image, and an object coordinate system determination unit 6 that determines an object coordinate system of a target object based on a plurality of marker coordinate systems. is there.
[Selection] Figure 2

Description

  The present invention relates to an estimation apparatus, an estimation method, and an estimation program for estimating an object coordinate system that indicates a three-dimensional position / posture of a target object in space using a marker.

A measuring device that captures an image of an object with a marker for position / posture identification and measures the three-dimensional position / posture of the object is disclosed (Patent Document 1, Non-Patent Document 1). In such a measurement apparatus, measurement error may occur because three-dimensional information is obtained from a two-dimensional image acquired by a camera.
In the method of Patent Document 1, three or more markers are pasted, and the position and orientation of the object are estimated using the three-dimensional point information of each marker. On the other hand, in the method of Non-Patent Document 1, one marker having three or more feature points is attached to one object.

JP 2003-254716 A

Image Understanding-Mathematics of 3D Recognition Kenichi Kanaya Morikita Publishing Co., Ltd. 1990 first edition published

  However, in the method of Patent Document 1, when the camera is close to an object, the marker is out of the field angle. If even one marker is removed, the position and orientation of the object cannot be calculated. That is, when the three markers do not fall within the angle of view, the position / posture cannot be estimated. Further, in the method of Non-Patent Document 1, since it must be attached to an object as one marker, the marker must be enlarged in order to estimate the position / posture from a distance with high accuracy. For example, depending on the object, the space for attaching the marker is limited. Therefore, it is difficult to estimate the position and orientation with high accuracy depending on the object and the imaging conditions.

  The present invention has been made in view of the above problems, and an estimation apparatus, an estimation method, and an estimation program capable of stably estimating an object coordinate system indicating a three-dimensional position / orientation of an object with high accuracy. The purpose is to provide.

  An estimation apparatus according to a first aspect of the present invention is an estimation apparatus that estimates an object coordinate system indicating a three-dimensional position / posture in a space of a target object having a plurality of markers, and is an object image obtained by imaging the target object To a marker detection unit that detects a marker that is provided on the target object and is capable of estimating a three-dimensional position and orientation by itself, and a plurality of first marker coordinates corresponding to the plurality of markers detected by the marker detection unit In order to calculate a system, a marker coordinate system estimation unit that estimates a first marker coordinate system from each marker image and an object coordinate system of the target object are determined based on the plurality of first marker coordinate systems. An object coordinate system determination unit. In such a configuration, since the object coordinate system can be estimated using a plurality of marker coordinate systems, it can be estimated with high accuracy.

  An estimation apparatus according to a second aspect of the present invention is the above estimation apparatus, wherein an object coordinate system is determined based on a plurality of first marker coordinate systems estimated from a marker image included in the object image. Temporarily determined, the temporarily determined object coordinate system is converted into a second marker coordinate system, the first marker coordinate system estimated from the marker image, and the second marker coordinates converted from the object coordinate system The object coordinate system is determined by minimizing an error with the system. Thereby, it can estimate with higher precision.

  An estimation device according to a third aspect of the present invention is the estimation device described above, wherein a plurality of the estimation devices are arranged such that the error between the first marker coordinate system and the second marker coordinate system is minimized. The object coordinate system is determined by optimizing the weight for the first marker coordinate system. Thereby, highly accurate estimation is attained by a simple method.

  An estimation apparatus according to a fourth aspect of the present invention is the above-described estimation apparatus, in which a Levenberg-Marquardt method is used for optimization of the weighting function. Thereby, it is possible to estimate with high accuracy in a short processing time.

  An estimation device according to a fifth aspect of the present invention is the above estimation device, and when the number of markers detected by the marker detection unit is one, the first marker coordinate system of the one marker From the above, the object coordinate system is estimated. As a result, stable estimation is possible regardless of the angle of view.

  An estimation method according to a sixth aspect of the present invention is an estimation method for estimating an object coordinate system indicating a three-dimensional position / posture in a space of a target object having a plurality of markers, and an object image obtained by imaging the target object The step of detecting a marker provided on the target object and capable of estimating a three-dimensional position / attitude alone, and a plurality of first marker coordinate systems corresponding to the plurality of markers detected by the marker detector A step of estimating a first marker coordinate system from each of the marker images and calculating an object coordinate system of the target object based on the plurality of first marker coordinate systems for calculation. It is. In such a configuration, since the object coordinate system can be estimated using a plurality of first marker coordinate systems, it can be estimated with high accuracy.

  An estimation method according to a seventh aspect of the present invention is the above estimation method, wherein an object coordinate system is calculated based on a plurality of first marker coordinate systems estimated from a marker image included in the object image. Temporarily determined, the temporarily determined object coordinate system is converted into a second marker coordinate system, the first marker coordinate system calculated from the marker image, and the second marker coordinates converted from the object coordinate system The object coordinate system is determined by minimizing a system error.

  An estimation method according to an eighth aspect of the present invention is the above estimation method, wherein a plurality of first methods are used so that the error between the first marker coordinate system and the second marker coordinate system is minimized. The object coordinate system is determined by optimizing the weighting function for one marker coordinate system.

  An estimation method according to a ninth aspect of the present invention is the above estimation method, in which the Levenberg-Marquardt method is used for optimization of the weighting function.

  The estimation method according to the tenth aspect of the present invention is the estimation method described above, wherein when the number of detected markers is one, the first marker coordinate system of the one marker The object coordinate system is estimated.

  An estimation program according to an eleventh aspect of the present invention is an estimation program for estimating an object coordinate system indicating a three-dimensional position / posture in a space of a target object having a plurality of markers, and Detecting a marker provided on the target object and capable of estimating a three-dimensional position / posture by itself, and a plurality of first corresponding to the plurality of markers detected by the marker detection unit. In order to calculate the marker coordinate system, a step of estimating a first marker coordinate system from each marker image, and a step of determining an object coordinate system of the target object based on the plurality of first marker coordinate systems Are provided.

  An estimation program according to a twelfth aspect of the present invention is the above estimation program, which is based on a plurality of first marker coordinate systems calculated from marker images included in the object image with respect to a computer. The object coordinate system is temporarily determined, the temporarily determined object coordinate system is converted into the second marker coordinate system, and the first marker coordinate system calculated from the marker image and the object coordinate system are converted. The object coordinate system is determined by minimizing the error of the second marker coordinate system.

  An estimation program according to a thirteenth aspect of the present invention is the above estimation program so that an error between the first marker coordinate system and the second marker coordinate system is minimized with respect to the computer. The object coordinate system is determined by optimizing the weights for the plurality of first marker coordinate systems.

  An estimation program according to a fourteenth aspect of the present invention is the above estimation program, in which the Levenberg-Marquardt method is used for optimization of the weighting function.

  An estimation program according to a fifteenth aspect of the present invention is the above estimation program, and when the number of detected markers is one, the first marker coordinate system of the one marker The object coordinate system is estimated. As a result, stable estimation is possible regardless of the angle of view.

  According to the present invention, it is possible to provide an estimation device, an estimation method, and an estimation program capable of estimating an object coordinate system indicating a three-dimensional position / attitude of an object with high accuracy.

It is a figure which shows the whole structure of the estimation system which estimates a three-dimensional position and attitude | position. It is a block diagram which shows the processing apparatus used for the estimation apparatus concerning embodiment of this invention. It is a figure for demonstrating the process process in the estimation method concerning embodiment of this invention. It is a figure for demonstrating the process process in the estimation method concerning embodiment of this invention. It is a figure for demonstrating the process process in the estimation method concerning embodiment of this invention. It is a figure for demonstrating the process process in the estimation method concerning embodiment of this invention. It is a figure for demonstrating the process process in the estimation method concerning embodiment of this invention. It is a figure for demonstrating the process process in the estimation method concerning embodiment of this invention. It is a figure for demonstrating the process process in the estimation method concerning embodiment of this invention. It is a conceptual diagram which shows the estimation method concerning embodiment of this invention.

  Hereinafter, embodiments of a moving body according to the present invention will be described in detail with reference to the drawings. However, the present invention is not limited to the following embodiments. In addition, for clarity of explanation, the following description and drawings are simplified as appropriate.

  A system for estimating a three-dimensional position / coordinate will be described with reference to FIG. The estimation system according to the present embodiment includes a camera 1 and a processing device 2. The object 10 is a target object that is a target for estimating a three-dimensional position / posture (x, y, z, roll angle, pitch angle, yaw angle). That is, the object 10 is imaged by the camera 1, and the three-dimensional position / orientation of the object 10 is estimated based on the object image. The target object 10 has a plurality of markers. In the present embodiment, an object coordinate system indicating a three-dimensional position / posture in the space of a target object having a plurality of markers is estimated.

  The camera 1 images an object that is a target for obtaining a three-dimensional position / coordinate. The camera 1 is, for example, a CCD camera and captures an object image including all or part of an object. Note that a stereo camera may be used as the camera 1. The object image acquired by the camera 1 is input to the processing device 2.

  The object 10 is provided with markers 11 and 12. In this example, two markers 11 and 12 are provided, but three or more markers may be provided on the object 10. Each of the markers 11 and 12 is an identification marker that can detect a three-dimensional position and posture by itself. For example, each marker 11 and 12 has three or more feature points. For example, the markers 11 and 12 have a square frame and a pattern provided in the frame when viewed from the front. The vertex of the square frame becomes the marker feature point. Further, each marker has a different shape, color, pattern, blinking, etc., and can be distinguished from other markers. Further, the positions and orientations of the markers 11 and 12 on the object 10 are known.

  The processing device 2 is, for example, a personal computer, and is an arithmetic processing device having a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), a communication interface, and the like. The processing device 2 also has a removable HDD, optical disk, magneto-optical disk, etc., stores various programs and control parameters, and supplies the programs and data to a memory (not shown) or the like as necessary. . Of course, the processing apparatus 2 is not limited to one physical configuration physically. The processing device 2 performs predetermined image processing on the object image data acquired by the camera 1. Thereby, the object coordinate system 30 indicating the three-dimensional position / posture of the object 10 in the three-dimensional space is estimated. The object coordinate system includes information on the X direction (horizontal direction) position, the Y direction (vertical direction) position, the Z direction (depth direction) position, the roll angle, the pitch angle, and the yaw angle. For example, the object coordinate system is indicated by a six-dimensional vector. With this object coordinate system, the three-dimensional position / posture of the object 10 in the space can be specified.

  Processing in the processing apparatus 2 that is one of the features of the present invention will be described with reference to FIGS. FIG. 2 is a block diagram showing a configuration of the processing device 2. FIG. 3 is a flowchart showing the processing method. 4 to 9 are diagrams for explaining each processing step. FIG. 10 is a conceptual diagram showing an estimation method according to the present embodiment. The processing device 2 includes a marker detection unit 3, a marker coordinate system estimation unit 4, a setting storage unit 5, an object coordinate system determination unit 6, and a coordinate system conversion unit 7.

  First, when an object is imaged by the camera 1, the object image is input to the processing device 2 (step S101). The processing device 2 stores the object image in a storage device such as a memory. Here, for example, it is assumed that the object image shown in FIG. 4 is input. Part of the object 10, part of the object 40, and part of the object 60 appear in one frame image acquired by the camera 1. Two markers 11 and 12 provided on the object 10 are included in the image. In addition, a marker 41 provided on the object 40 is included in the image. Similarly, a marker 61 provided on the object 60 is included in the image. In the following description, an example of estimating the three-dimensional position / posture of the object 10 in which the two markers 11 and 12 are imaged will be mainly described.

  The marker detection unit 3 detects a marker from the object image acquired by the camera 1 (step S102). Thereby, a plurality of marker images are extracted from the object image. Here, a portion surrounded by a dotted frame shown in FIG. 4 is extracted as a marker image. Since each marker has a unique pattern, color, and the like, each marker can be distinguished. For example, the setting storage unit 5 stores setting information such as unique patterns and colors in association with each other. By referring to the setting information, the marker detection unit 3 can specify which marker of which object each marker image is.

  Then, the three-dimensional position / posture of each marker is estimated (step S103). Here, the marker three-dimensional positions and postures of the marker 11, the marker 12, the marker 41, and the marker 61 are estimated. Here, a first marker coordinate system indicating a three-dimensional position / posture is calculated. The marker coordinate system estimation unit 4 estimates the first marker coordinate system of each marker. For example, the first marker coordinate system can be calculated using a vector between a plurality of marker feature points. Here, as shown in FIG. 5, the first marker coordinate system 21 is calculated from the marker image of the marker 11. Similarly, the first marker coordinate system 22 is calculated from the marker image of the marker 12, the first marker coordinate system 51 is calculated from the marker image of the marker 41, and the first marker coordinate system 71 is calculated from the marker image of the marker 61. Is calculated. The marker coordinate system indicates positions on the X axis, Y axis, and Z axis, and directions of the X axis, Y axis, and Z axis. With this marker coordinate system, the position / posture of the marker in the space can be specified. In addition, about step S103 and step S102, the various calculation methods shown by the nonpatent literature 1 can be used, for example.

  Then, it is determined whether or not a plurality of markers are detected for one object (step S104). As shown in FIG. 6, since only one marker 41 has been detected for the object 40, the process proceeds to NO in step S104. Similarly, since only one marker 61 is detected for the object 60, the process proceeds to NO in step S104. In the objects 40 and 60, the object coordinate system is determined by one marker (step S108). That is, the first marker coordinate system is converted to the object coordinate system. Since the position / orientation of the marker 41 on the object 40 is known, the object coordinate system can be easily determined by using the transformation matrix. Thereby, an estimation process is complete | finished. This conversion matrix is stored in the setting storage unit 5 in advance. That is, since this process is the same as a well-known process, description is abbreviate | omitted.

  When there are a plurality of markers detected for one object, the object coordinate system determination unit 6 provisionally determines the object coordinate system (step S105). For example, since the two markers 11 and 12 are detected for the object 10, the process proceeds to step S105. As shown in FIG. 7, the object coordinate system 30a is provisionally determined based on the two first marker coordinate systems 21 and 22. The temporarily determined object coordinate system is defined as an object coordinate system 30a. An example of this provisional determination will be described.

  First, the weight for each marker is obtained by equation (1), and a solution (object coordinate system) is provisionally determined by equation (2).

In this way, the object coordinate system is provisionally determined by the weighted average. The weight is a function of the depth distance of the object 10 with respect to the camera 1, the size of the marker, the roll angle, the pitch angle, and the yaw angle. A marker closer to the camera is heavier, a larger marker is heavier, and a marker with a smaller rotation angle is heavier. Thus, the weight of each marker is obtained from the marker image. The method for calculating the initial value of the weight is not particularly limited. The temporary object coordinate system includes a measurement error by the camera 1. Further, since the relative position between the object and the marker is known, the transformation matrix K _i from the marker coordinate system to the object coordinate system is known. That is, since the relative positions of the marker and the object are determined in advance, a conversion matrix between the marker coordinate system and the object coordinate system can be set in advance. The conversion matrix for each marker is stored in the setting storage unit 5. In Expression (2), the number of markers is generalized as n (2 or more natural numbers). In the case of the object 10, n = 2.

  Next, a second marker coordinate system is calculated from the provisionally determined object coordinate system 30a (step S106). Here, the coordinate system conversion unit 7 converts the temporarily determined object coordinate system into the second marker coordinate system. Thereby, the second marker coordinate system of the plurality of markers is calculated based on one object coordinate system. As shown in FIG. 8, second marker coordinate systems 21a and 22a for the markers 11 and 12 are obtained from the object coordinate system 30a. Specifically, the second marker coordinate systems 21a and 22a can be calculated by Expression (3).

  Since the relative position between the object and the marker is known, the conversion matrix for converting the object coordinate system to the second marker coordinate system is known. Of course, the transformation matrix is different for each marker. Here, the second marker coordinate systems 21a and 22a are calculated from the object coordinate system 30a provisionally determined using the weighted average. Therefore, the first marker coordinate systems 21 and 22 calculated from the camera marker image are different from the second marker coordinate systems 21a and 22a estimated from the object coordinate system. In other words, it can be said that the marker coordinate system includes an error.

  The error between the detected first marker coordinate system and the second marker coordinate system estimated from the object coordinate system determined in consideration of the weight can be calculated as follows. In general, an error between the first marker coordinate system and the second marker coordinate system can be expressed by a difference between the marker coordinate systems as shown in the following equation (4).

  Here, the error between the first marker coordinate system and the second marker coordinate system can be expressed as a three-dimensional space error or a screen projection error. The three-dimensional space error is an error in each of the three-dimensional position and orientation, and can be represented as a six-dimensional vector. Substituting the three-dimensional position / posture (distance / angle) of the second marker coordinate system estimated from the object coordinate system and the detected position / posture (distance / angle) of the first marker coordinate system into the evaluation formula 3D space error. It should be noted that since different indices such as distance and angle are included in one evaluation formula, it is necessary to define the evaluation formula appropriately.

  The screen projection error is an error of the projection point of the marker feature point and can be shown as a pixel in the camera image. That is, the marker feature point is obtained from the position / posture of the second marker coordinate system estimated from the object coordinate system. An image coordinate point obtained by projecting the marker feature point onto the camera image is calculated. That is, a marker feature point is projected onto a two-dimensional camera image using a projection matrix. The difference between the calculated image coordinate point and the image coordinate point of the marker feature point obtained from the camera image (distance on the image) is defined as a screen projection error. Note that the projection matrix can be obtained from the focal length of the camera and the distortion of the lens.

Next, it is determined whether or not the error of the object coordinate system is minimum (step S107). That is, the processes in steps S105 to S107 are repeatedly executed until the error is minimized. When the error is minimized, the process is terminated. Thereby, as shown in FIG. 9, the object coordinate system 30b is decided. Specifically, as shown in FIG. 10, optimization is performed so that the error of the object coordinate system is minimized. The following calculation is repeated until the error converges. (1) The object coordinate system is obtained from the first marker coordinate system by weighted averaging. (2) The object coordinate system is converted to the second marker coordinate system. (3) Update the weighting function to reduce the error.
The processes (1) to (3) are repeated to minimize the error. By doing in this way, the weighting function shown by Formula (1) can be optimized, and an error can be minimized. Therefore, it is possible to estimate the three-dimensional position / posture with high accuracy.

  By solving the weighted least squares method by iterative calculation, the position and orientation can be estimated with high accuracy. Since solving the weighted least square method is a nonlinear optimization problem, in the present embodiment, the variable is updated using the Levenberg-Marquardt method to find the solution of Equation (5).

  Here, the error is the screen projection error shown by Expression (4). Iterative calculation is performed so that the sum of squares of the screen projection error is minimized. Thereby, the weight for the first marker coordinate system can be optimized. Therefore, the position / orientation can be calculated with high accuracy.

  Further, by using the Levenberg-Marquardt method, it is possible to perform highly accurate estimation in a short time. Thereby, processing time can be shortened. In the case of minimizing the three-dimensional space error, the three-dimensional space error represented by the equation (4) is obtained for each marker, and the sum of squares thereof is minimized. Even in this case, it is possible to estimate the three-dimensional position / posture with high accuracy.

  When the object 10 and the camera 1 are far from each other, a plurality of markers fall within the angle of view of the camera 1. Therefore, the position / posture can be estimated from a plurality of markers. By using a plurality of markers, highly accurate estimation is possible. When the camera 1 and the object 10 are close to each other, the three-dimensional position / posture by one marker can be detected. That is, even when only one marker can be accommodated in the angle of view of the camera 1, since one marker has three or more feature points, the position / orientation can be estimated. When the camera 1 is close to the object 10, a large marker can be used, so that high-precision estimation is possible.

  Thus, by performing position estimation based on the marker included in the camera image, highly accurate estimation can be stably performed. That is, when the distance between the object and the camera is far, the accuracy can be improved by estimation with a plurality of markers. When the distance is close, one marker becomes a large marker image, so the accuracy can be improved even with a small number of markers. Can do. Therefore, it is possible to estimate with high accuracy even when the distance is far or near. Note that the arrangement of the markers and the size of the markers may be determined according to the camera to be used, the space, the size of the object, the shape of the object, and the like. Further, the number of markers provided on the object is not particularly limited, but a larger number is preferable. In other words, the estimation accuracy can be improved by having more markers within one angle of view.

  Such an estimation device is preferably mounted on a robot. By mounting the estimation device on a robot having an arm that grips an object, the object can be reliably gripped. In particular, it is suitable for industrial robots that hold objects and household robots. Furthermore, it is also suitable for facility management purposes in factories.

  In the above description, the error is minimized by the weighted least square method, but the error may be minimized by using another method. Furthermore, the method for obtaining the object coordinate system from the plurality of first marker coordinate systems is not particularly limited.

  The above estimation process may be executed by a computer program. A program including a group of instructions for causing a computer to perform three-dimensional / position / posture estimation processing can be supplied to a computer using a non-transitory computer readable medium. Non-transitory computer readable media include various types of tangible storage media. For example, the non-transitory computer readable medium is a magnetic storage medium (eg, flexible disk, magnetic tape, hard disk drive), magneto-optical storage medium (eg, magneto-optical disk), CD-ROM, CD-R, CD-R / W. RAM (Random Access Memory), ROM (Read Only Memory), UV-EPROM (Erasable ROM), EEPROM (Electrical EPROM), and flash ROM. The program may be supplied to the computer by a non-transitory computer readable medium. Temporary media include electrical signals, optical signals, and electromagnetic waves encoded with a program. An electrical signal, an optical signal, and an electromagnetic wave encoded with a program are supplied to a computer by propagating through a wired transmission path such as an electric wire and an optical fiber, or a wireless transmission path (space).

DESCRIPTION OF SYMBOLS 1 Camera 2 Processing apparatus 10 Object 11 Marker 12 Marker 21 1st marker coordinate system 21a 2nd marker coordinate system 22 1st marker coordinate system 22a 2nd marker coordinate system 30 Object coordinate system 40 Object 41 Marker 51 1st Marker coordinate system 60 object 60 object 61 marker 71 first marker coordinate system

Claims (15)

An estimation apparatus for estimating an object coordinate system indicating a three-dimensional position / posture in a space of a target object having a plurality of markers,
A marker detection unit that detects a marker provided on the target object and capable of estimating a three-dimensional position and orientation by itself from an object image obtained by imaging the target object;
A marker coordinate system estimation unit for estimating a first marker coordinate system from each marker image in order to calculate a plurality of first marker coordinate systems corresponding to the plurality of markers detected by the marker detection unit;
An estimation apparatus comprising: an object coordinate system determination unit that determines an object coordinate system of the target object based on the plurality of first marker coordinate systems. Tentatively determining an object coordinate system based on a plurality of first marker coordinate systems estimated from a marker image included in the object image;
Converting the provisionally determined object coordinate system to a second marker coordinate system;
The object coordinate system is determined by minimizing an error between a first marker coordinate system estimated from the marker image and a second marker coordinate system converted from the object coordinate system. Estimating device.   The object coordinate system is determined by optimizing a weighting function for a plurality of marker coordinate systems so that the error between the first marker coordinate system and the second marker coordinate system is minimized. The estimation apparatus described in 1.   The estimation apparatus according to claim 3, wherein a Levenberg-Marquardt method is used for optimization of the weighting function. When the number of markers detected by the marker detection unit is one,
The estimation apparatus according to claim 1, wherein the object coordinate system is estimated from the first marker coordinate system of the one marker. An estimation method for estimating an object coordinate system indicating a three-dimensional position / posture in a space of a target object having a plurality of markers,
Detecting a marker provided on the target object and capable of estimating a three-dimensional position / orientation alone from an object image obtained by imaging the target object;
Estimating a first marker coordinate system from each marker image in order to calculate a plurality of first marker coordinate systems corresponding to the plurality of markers detected by the marker detection unit;
Determining an object coordinate system of the target object based on the plurality of first marker coordinate systems. Tentatively determining an object coordinate system based on a plurality of first marker coordinate systems estimated from a marker image included in the object image;
Converting the provisionally determined object coordinate system to a second marker coordinate system;
The object coordinate system is determined by minimizing an error between a first marker coordinate system calculated from the marker image and a second marker coordinate system converted from the object coordinate system. Estimation method.   The object coordinate system is determined by optimizing a weighting function for a plurality of marker coordinate systems so that the error between the first marker coordinate system and the first marker coordinate system is minimized. The estimation method described in 1.   The estimation method according to claim 8, wherein a Levenberg-Marquardt method is used for optimization of the weighting function. When the number of detected markers is one,
The estimation method according to claim 6, wherein the object coordinate system is estimated from a first marker coordinate system of the one marker. An estimation program for estimating an object coordinate system indicating a three-dimensional position / posture in a space of a target object having a plurality of markers,
Against the computer,
Detecting a marker provided on the target object and capable of estimating a three-dimensional position / posture alone from an object image obtained by imaging the target object;
A step of estimating the first marker coordinate system marker coordinate system from the respective marker images in order to calculate the plurality of first marker coordinate system marker coordinate systems corresponding to the plurality of markers detected by the marker detection unit; When,
An estimation program comprising: determining an object coordinate system of the target object based on the plurality of first marker coordinate system marker coordinate systems. Against the computer,
The object coordinate system is provisionally determined based on the plurality of first marker coordinate system marker coordinate systems calculated from the marker image included in the object image,
Converting the temporarily determined object coordinate system into a second marker coordinate system;
12. The object coordinate system is determined by minimizing an error between a first marker coordinate system calculated from the marker image and a second marker coordinate system converted from the object coordinate system. Estimation program. Against the computer,
The object coordinate system is determined by optimizing a weight for a plurality of marker coordinate systems so that an error between the first marker coordinate system and the second marker coordinate system is minimized. Estimation program.   The estimation program according to claim 13, wherein a Levenberg-Marquardt method is used for the optimization of the weights. When the number of detected markers is one,
The estimation program according to claim 11, wherein the object coordinate system is estimated from a first marker coordinate system of the one marker.

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