JP2015031601A - Three-dimensional measurement instrument, method, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To measure a three-dimensional position of an object or the like without increasing a measurement error by using input images captured by one camera.SOLUTION: Measuring a three-dimensional position of a measurement object from input images includes: changing a position relation between a mirror and a camera without changing a relative position relation between the camera and the measurement object to acquire, as input images, a plurality of images captured through the mirror by the camera; calculating mirror plane coordinates on the basis of positions of a feature pattern in the input images and the focal length of the camera; calculating a camera coordinate system of a mirror space obtained by reflection transformation of camera coordinates with a mirror plane as the center; using positions of the measurement object in the input images to calculate beams indicative of the direction of the measurement object, from the camera coordinates; calculating, as virtual beams, vectors obtained by reflection transformation of the beams with a virtual camera coordinate origin as the start point; and calculating an intersection among a plurality of virtual beams as the position of the measurement object.

Description

  The present invention relates to a technique for measuring a three-dimensional position of an object or the like by image analysis.

  Conventionally, a method using stereo vision is known as a three-dimensional measurement method. As an existing technology, Patent Document 1 not only captures a real image of an object using a movable stereo camera, but also captures a virtual image reflected in a mirror that reflects the object, and uses the real image and the virtual image to capture the object. A technique for measuring a three-dimensional shape is disclosed. In Patent Document 2, an electronic camera, a movable mirror, and two markers are prepared, the position of the projection point of the marker on the imaging surface of the electronic camera is detected, the position of the camera, the position of the marker, the attitude of the movable mirror, and the projection A method is disclosed in which the orientation of a camera is calculated based on the position of a point and the stereo camera is reinstated for stereo viewing.

JP 2001-338278 A JP 2012-220356 A

  In a conventional three-dimensional measurement method using stereo vision, position and orientation measurement using a feature pattern has been performed as calibration in order to obtain a relationship between cameras. The posture value between the cameras greatly affects the three-dimensional measurement result of the measurement object. In particular, there is a problem that the posture error when the feature pattern is observed from the front of the camera with a camera becomes large, resulting in a large error in the measurement result.

  When a plurality of cameras are installed, the position and orientation relationship between the cameras is calculated from the feature pattern every time a measurement environment is created. There is a problem that such preparation is troublesome.

  In the conventional three-dimensional object measurement method using a mirror, first, a feature pattern is attached to the mirror, and the mirror plane position is obtained by observing the feature pattern on the mirror plane from the camera. At this time, the direction of the mirror is changed while photographing the measurement object with the camera through the mirror. Then, the position of the measurement object is obtained by stereo vision from the positions of the plurality of mirror planes and the position of the measurement object reflected on the mirror.

  At this time, as in the general stereo vision method, the posture measurement of the mirror plane by the feature pattern pasted on the mirror greatly affects the measurement result of the measurement object. In particular, there is a problem that the posture error when the feature pattern is observed from the front of the camera with a camera becomes large, resulting in a large error in the measurement result.

  Further, the mirror has a protective layer made of glass or acrylic on the mirror surface portion where reflection occurs. The feature pattern plane affixed to the protective layer is separated from the actual mirror surface portion by a distance corresponding to the thickness of the protective layer. Therefore, there is a problem that an error corresponding to the thickness occurs in the measurement of the planar position of the mirror.

  The present invention has been made in view of the above circumstances, enables measurement of a three-dimensional position of an object without using a plurality of cameras, improves measurement accuracy over conventional stereo vision techniques, An object of the present invention is to provide an apparatus, a method, and a program that make it possible to simplify installation work of a measurement environment.

  The three-dimensional measuring device of the present invention is a device that measures the position of a measurement object from an input image, and the input image is an image captured by a camera through a mirror, and the position and orientation relationship from the measurement object to the camera A plurality of images captured with a predetermined feature pattern having a predetermined relationship, a fixed relative positional relationship between the camera and the measurement object, and a variable positional relationship between the mirror and the camera as the input image. The center position of the feature pattern in the mirror space calculated based on the position of the feature pattern input and reflected in the input image and the focal length of the camera, and the center position of the feature pattern in the real space known from the camera. By mirror transformation, the midpoint of the line segment connecting the center point of the real space feature pattern and the mirror space feature pattern is the origin of the mirror plane coordinates, and a vector parallel to the line segment is one of the mirror plane coordinates. A mirror plane that calculates a plane that passes through the mirror plane coordinate origin and is perpendicular to the coordinate axis as a mirror plane, and calculates a mirror plane coordinate represented by two coordinate axes arbitrarily set on the coordinate axis and the mirror plane A coordinate calculation means, a virtual camera coordinate calculation means for calculating a camera coordinate system in a mirror space obtained by mirror-transforming the camera coordinates around the mirror plane, and a measurement object from the camera coordinates using the position of the measurement object in the input image A light ray calculating means for calculating a light ray indicating the direction of the light source, and a virtual light ray calculating means for calculating, as a virtual light ray, a vector obtained by mirror-transforming the light ray with the virtual camera coordinate origin as a starting point and the mirror plane as a center. Virtual ray intersection calculation means for calculating an intersection of a plurality of virtual rays calculated based on each of the input images as a position of the measurement object.

  The three-dimensional measurement method of the present invention is a method of measuring the position of a measurement object from an input image, wherein the input image is an image captured through a mirror by a camera, and the position and orientation relationship from the camera A plurality of images captured with a predetermined feature pattern having a predetermined relationship, a fixed relative positional relationship between the camera and the measurement object, and a variable positional relationship between the mirror and the camera as the input image. The center position of the feature pattern in the mirror space calculated based on the position of the feature pattern input and reflected in the input image and the focal length of the camera, and the center position of the feature pattern in the real space known from the camera. By mirror transformation, the midpoint of the line segment connecting the center point of the real space feature pattern and the mirror space feature pattern is the origin of the mirror plane coordinates, and a vector parallel to the line segment is one of the mirror plane coordinates. A plane that passes through the mirror plane coordinate origin and is perpendicular to the coordinate axis as a mirror plane, and calculates a mirror plane coordinate represented by two coordinate axes arbitrarily set on the coordinate axis and the mirror plane; Calculating a camera coordinate system in a mirror space obtained by mirror-transforming camera coordinates around the mirror plane, and calculating a ray indicating the direction of the measurement object from the camera coordinates using the position of the measurement object in the input image. And a step of calculating, as a virtual ray, a vector obtained by mirror-transforming the ray with the virtual camera coordinate origin as a starting point, and a plurality of virtual images calculated based on each of a plurality of input images Calculating the intersection of the rays as the position of the measurement object.

  The three-dimensional measurement program of the present invention is a program that causes a computer to measure the position of a measurement object from an input image, and the input image is an image captured by a camera through a mirror. A predetermined feature pattern in which the position and orientation relationship is a predetermined relationship is shown, and a plurality of images captured with the relative positional relationship between the camera and the measurement object fixed and the positional relationship between the mirror and the camera being variable are described above. The center position of the feature pattern in the mirror space that is input as an input image and calculated based on the position of the feature pattern reflected in the input image and the focal length of the camera, and the center of the feature pattern in the real space that is known from the camera With respect to the position, by mirror conversion, the midpoint of the line segment connecting the center point of the real space feature pattern and the mirror space feature pattern is the origin of the mirror plane coordinates, and the line segment A line vector is defined as one coordinate axis of mirror plane coordinates, a plane passing through the mirror plane coordinate origin and perpendicular to the coordinate axis is calculated as a mirror plane, and is expressed by two coordinate axes arbitrarily set in the coordinate axis and the mirror plane. A step of calculating a mirror plane coordinate to be calculated, a step of calculating a camera coordinate system of a mirror space obtained by mirror-transforming the camera coordinate around the mirror plane, and a measurement from the camera coordinate using the position of the measurement object in the input image A step of calculating a ray indicating the direction of the object, and a step of calculating, as a virtual ray, a vector obtained by mirror-transforming the ray with the virtual camera coordinate origin as a starting point and the mirror plane as a center. Calculating the intersection of a plurality of virtual rays calculated based on the position of the measurement object, and causing the computer to execute the step. .

Here, the intersection of the virtual rays is calculated by calculating a normal line composed of direction vectors of two rays when the rays do not intersect with each other, calculating a line segment connecting two rays parallel to the normal line, and The midpoint may be the intersection.
Further, when there are two or more virtual rays, the positions of the centers of gravity of a plurality of intersections of combinations of the two rays may be calculated as the positions of the measurement objects.

  According to the present invention, an apparatus for measuring the position of a measurement object from an input image, the input image is an image captured by a camera through a mirror, and the position and orientation relationship from the camera is a predetermined relationship A predetermined feature pattern is shown, and the center position of the feature pattern in the mirror space calculated based on the position of the feature pattern shown in the input image and the focal length of the camera, and the real space known from the camera With respect to the center position of the feature pattern, by mirror conversion, the midpoint of the line connecting the feature pattern in the real space and the center point of the feature pattern in the mirror space is the origin of the mirror plane coordinates, and a vector parallel to the line segment is the mirror plane Calculate as a single coordinate axis of coordinates, a plane passing through the mirror plane coordinate origin and perpendicular to the coordinate axis as a mirror plane, and calculate a mirror plane coordinate represented by two coordinate axes arbitrarily set in the coordinate axis and the mirror plane A plane coordinate calculation means, a virtual camera coordinate calculation means for calculating a camera coordinate system in a mirror space obtained by mirror-transforming camera coordinates around a mirror plane, and a measurement object from the camera coordinates using the position of the measurement object in the input image A plurality of input images, comprising: a ray calculation means for calculating a ray indicating the direction of the light; and a virtual ray calculation means for calculating as a virtual ray a vector obtained by mirror-converting the ray centered on a mirror plane with a virtual camera coordinate origin as a starting point. By providing virtual ray intersection calculation means for calculating the intersection of a plurality of virtual rays calculated based on each as the position of the measurement object, it is possible to improve measurement accuracy.

  In addition, since the input images are a plurality of images captured by changing the positional relationship between the mirror and the camera without changing the relative positional relationship between the camera and the measurement object, the three-dimensional position of the object is measured without using a plurality of cameras. In addition, it is possible to simplify the installation work of the input image capturing environment.

It is a schematic diagram of the three-dimensional measuring apparatus which shows embodiment of this invention. It is a block diagram which shows the structure of the three-dimensional measuring apparatus which shows embodiment of this invention. It is a figure which shows the relationship between the coordinate system of real space and mirror space in mirror conversion. It is a flowchart explaining the process sequence of this invention. It is a figure which shows the image which imaged the characteristic pattern and the measurement object through the mirror. It is a figure which shows the center position of the virtual feature pattern of the camera of real space and mirror space. It is a figure which shows the relationship between the center position of the feature pattern of real space and mirror space, and a mirror plane coordinate system. It is a figure which shows the light ray extended from the camera coordinate of real space to a virtual measurement object. It is a figure which shows the virtual ray extended to the measurement object from the virtual camera coordinate of mirror space. It is FIG. (1) which shows the virtual ray calculated from a different input image. It is FIG. (2) which shows the virtual ray calculated from a different input image. It is a figure which shows the intersection of the virtual ray calculated from a different input image. It is a figure which shows the measurement object calculated as an intersection when virtual rays do not cross. It is a figure which shows the measurement object calculated as a gravity center position of each intersection when there exist two or more virtual rays. It is a schematic diagram of the three-dimensional measuring apparatus using the circle feature pattern used as another embodiment of the present invention. It is a figure which shows the relationship between the center position of the circular feature pattern of real space and mirror space, and a mirror plane coordinate system. It is a schematic diagram of the three-dimensional measuring apparatus using the portable terminal used as another embodiment of this invention. It is a schematic diagram of a posture correction system for a humanoid robot as an application example of the present invention.

  Hereinafter, a three-dimensional measuring apparatus according to an embodiment of the present invention will be described with reference to the drawings. Specifically, a case where the position of a marker (measurement object) is measured as an example of three-dimensional position measurement will be described. FIG. 1 is a schematic diagram of a three-dimensional measuring apparatus showing an embodiment of the present invention, and FIG. 2 is a block diagram showing a configuration of the three-dimensional measuring apparatus showing an embodiment of the present invention.

  As shown in FIG. 1, in the embodiment of the present invention, a chess board pattern is mounted on a three-dimensional measuring device 3 as a camera 1 and a feature pattern 2. Here, it is assumed that the position and orientation relationship between the coordinate system of the camera 1 and the coordinate system of the feature pattern 2 is known. In addition, the three-dimensional measurement apparatus 3 includes an image input unit 11 that acquires an image captured by the camera 1, a mirror plane coordinate calculation unit 12, a virtual camera coordinate calculation unit 13, a light ray calculation unit 14, and a virtual ray as illustrated in FIG. 2. A calculation unit 15 and a virtual ray intersection calculation unit 16 are provided. An image acquired from the camera 1 via the image input unit 11 can be temporarily stored in a storage unit (not shown). Further, the processing program executed in each calculation unit described above is also stored in the storage unit, and this program is executed by a calculation unit (not shown).

In the present embodiment, when there are two coordinate systems A1 and A2, a homogeneous transformation matrix for transforming the coordinate system from A1 to A2 is expressed as in Equation 1.

FIG. 3 shows mirror conversion, and a coordinate system obtained by mirror conversion of A1 and A2 is represented as A1 'and A2'. Although A1 'and A2' are expressed in the left-handed coordinate system, as shown in Equation 2, the homogeneous transformation matrix from A1 'to A2' is equal to the homogeneous transformation matrix from A1 to A2.

  Next, a processing procedure for performing marker position measurement by the three-dimensional measurement apparatus according to the present embodiment will be described using the flowchart of FIG. FIG. 5 is an image captured by the camera 1. The camera 1 of the three-dimensional measuring apparatus 3 is captured in front of the mirror so that the feature pattern and the measurement object are reflected using specular reflection. An image captured by the camera 1 is read (step S1).

  As shown in FIG. 6, in this embodiment, the camera coordinate system is defined as C, the feature pattern coordinate system is defined as B, and the mirror-transformed C and B are represented as C ′ and B ′. A feature pattern coordinate system calculated from external parameters of the camera is represented by D. The external parameter is a parameter representing the posture relationship and the translational position relationship from the camera coordinates in the real space to the feature pattern coordinates.

  The coordinate system B is the center position of the feature pattern, and the x and y coordinate axes are axes along the feature pattern surface. The relative positions of the camera coordinate system and the feature pattern coordinate system are fixed, and the homogeneous transformation matrix CTB is known.

  Based on the position of the feature pattern in the input image, a coordinate system D of the mirrored feature pattern is calculated from the camera coordinates C to obtain CTD. CTB 'is calculated as the center position B' of the virtual feature pattern.

  More specifically, the number of grid points and the length of one side of the chessboard pattern are stored in advance, and information such as focal length, pixel size, and lens distortion, which is called an internal parameter of the camera, is also stored in advance. Has been. A coordinate position relationship (external parameter) is obtained from these pieces of information and the positions of lattice points in the actually captured image.

Here, for example, a coordinate position relationship is set, and if it is the coordinate position relationship at that time, the reprojection calculation is performed using the internal parameters where the lattice points of the chessboard pattern appear in the image. The external parameter is corrected by comparing the position of the lattice point projected in the image with the positional relationship of the actually captured lattice point. The calculation of the external parameter is repeated until the position of the lattice point in the actual image is the same as the position of the lattice point estimated by the parameter. Then, the coordinate position relationship is obtained by this iterative calculation.
In the present embodiment, the Zhang method is used.
(See Zhang Z., “A flexible new technique for camera calibration”, Transactions on Pattern Analysis and Machine Intelligence, 22 (11), pp. 1330-1334, 2000.)

Subsequently, when the coordinate origins of the coordinate systems B and B ′ are set to b and b ′, they can be expressed as Expression 3. Cb is a coordinate origin represented by the coordinate system C, and b ′ is a mirror point of b.

Regarding the positional relationship between the b and b ′ mirror planes, the midpoint between b and b ′ passes through the mirror plane due to the mirror conversion relationship. The normal vector of the mirror plane and the line segment b′-b are parallel. The mirror plane is calculated from this relationship.
As shown in Equation 4, the coordinate origin of the mirror plane coordinate system M 1 can be calculated from the midpoint between b and b ′.

  As shown in Equation 5a, the z-axis of the mirror plane coordinate system can be calculated as a parallel line of the line segment b'-b. In the present embodiment, the x-axis of the mirror plane coordinate system is calculated as a line parallel to the line segment obtained by projecting the x-axis of the camera coordinate system C onto the mirror plane, as shown in Expression 5b. As shown in Equation 5c, the y-axis of the mirror plane coordinate system is calculated from the outer product of the x and z axes of the mirror plane coordinate system. From these equations 5a-c, the mirror plane coordinate system can be expressed as equation 5.

As shown in FIG. 7, the mirror plane coordinate system is defined as M, and the position and orientation M of the mirror plane is calculated from the center position B ′ of the feature pattern and the actual center position B of the chess board (step S2).

When the coordinate origins of the camera coordinate system C and the virtual camera coordinate system C ′ are represented in the mirror plane coordinate system M, these coordinate origins are in a relationship in which the value of the z axis is inverted between positive and negative, so that the homogeneous transformation matrix MTC And MTC ′ can be expressed as in Equation 6.
Therefore, the homogeneous transformation matrix CTC ′ from the camera coordinate system to the virtual camera coordinate system can be expressed as Equation 7 (step S3).

FIG. 8 shows a light ray r. A pixel having the color information is identified from the image using color information of a marker that is known in advance, and an area having the color information is identified by a labeling process. Then, the barycentric point of the region is calculated as the marker position in the input image, and the ray r pointing to the marker is calculated from the camera coordinate system origin using the camera internal parameters.

As shown in FIG. 9, a virtual ray r ′ that is symmetrical with the ray in step S4 is calculated across the mirror plane in step S3. Due to the mirror transformation, the light rays extending from the virtual camera coordinate system in the mirror space pass through the marker in the real space. Therefore, the virtual ray r ′ matches the ray r. Further, since the coordinate system C and the coordinate system C ′ are symmetrical, it can be expressed as C′r ′ = Cr, and can be expressed as shown in Equation 8.

The virtual ray r ′ expressed in the camera coordinate system C can be expressed as Expressions 7 and 8 to Expression 9 (Step S5).

As shown in FIGS. 10A and 10B, the virtual ray r ′ in step S5 is obtained from the captured image by changing the positional relationship between the mirror and the camera 1 without changing the relative positional relationship between the camera 1 and the measurement object P. Calculate
As shown in FIG. 11, the position of the measurement object P is calculated from the intersection of the plurality of virtual rays r ′ calculated in step 4 (step S6).

At the time of step S5, when the virtual rays do not intersect as shown in FIG. 12, the shortest point between the virtual rays is calculated as the intersection. When there are two or more virtual rays as shown in FIG. 13, the positions of the centers of gravity of the intersections of the combinations of the two rays are calculated as the positions of the measurement objects.
In this way, the processes in steps S2 to S5 are repeated for a plurality of input images, the intersection of virtual rays is calculated in step S6, and the marker position is calculated.

  In this embodiment, a chess pattern is used as the feature pattern 2. However, in order to obtain mirror coordinates in step S3, it is only necessary to obtain the position information of the feature pattern in step S2. FIG. 14 shows a three-dimensional measuring apparatus in which the relationship between the center position of the circle pattern 20 of a known size and the camera coordinates is known. By measuring the center position of a circle pattern of a known size, mirror coordinates can be calculated as shown in FIG. The three-dimensional measuring apparatus can be reduced in size by the feature pattern using the circular pattern and the arrangement of the cameras. As a result, the three-dimensional measuring apparatus can be mounted on a digital camera or the like to perform object measurement.

  Further, by displaying the feature pattern on the screen of the mobile phone as shown in FIG. 16, the mobile phone can be used as a three-dimensional measuring device. Thereby, 3D data of a 3D printer or a CG model can be easily measured.

  Furthermore, as a calibration method for an object outside the camera field of view attached to the camera, it can be used for posture calibration (FIG. 17) of an arm or a humanoid robot or sensor calibration of a mobile robot.

  From the above, according to the present embodiment, it is possible to perform measurement with higher accuracy than the conventional method using stereo vision, and to simplify the installation work of the measurement environment and perform three-dimensional measurement of the measurement object. it can.

1 Camera 2 Feature pattern (chess board)
3 Three-dimensional measuring device 11 Image acquisition unit 12 Mirror plane coordinate calculation unit 13 Virtual camera coordinate calculation unit 14 Ray calculation unit 15 Virtual ray calculation unit 16 Virtual ray intersection calculation unit 20 Circle feature pattern

Claims (9)

An apparatus for measuring the position of a measurement object from an input image,
The input image is an image captured by a camera through a mirror, and the measurement object and a predetermined feature pattern in which a position and orientation relationship from the camera is a predetermined relationship are reflected,
The relative positional relationship between the camera and the measurement object is fixed, and a plurality of images captured as variable positional relationship between the mirror and the camera are input as the input image,
About the center position of the feature pattern in the mirror space calculated based on the position of the feature pattern reflected in the input image and the focal length of the camera, and the center position of the feature pattern in the real space known from the camera,
By mirror conversion, the midpoint of the line segment connecting the center point of the real space feature pattern and the mirror space feature pattern is the origin of the mirror plane coordinates, and the vector parallel to the line segment is one coordinate axis of the mirror plane coordinates. Mirror plane coordinate calculating means for calculating a plane passing through the mirror plane coordinate origin and perpendicular to the coordinate axis as a mirror plane, and calculating a mirror plane coordinate represented by two coordinate axes arbitrarily set on the coordinate axis and the mirror plane When,
Virtual camera coordinate calculation means for calculating a camera coordinate system of a mirror space obtained by mirror-converting camera coordinates around the mirror plane;
Ray calculation means for calculating a ray indicating the direction of the measurement object from the camera coordinates using the position of the measurement object in the input image;
Virtual ray calculation means for calculating as a virtual ray a vector obtained by mirror-transforming the ray around the mirror plane with the virtual camera coordinate origin as a starting point;
A three-dimensional measurement apparatus comprising: a virtual ray intersection calculation unit that calculates an intersection of a plurality of virtual rays calculated based on each of a plurality of input images as a position of a measurement object. When the light rays do not intersect, the intersection of the virtual rays is calculated as a normal line composed of two light beam direction vectors, a line segment connecting two light rays parallel to the normal line is calculated, and a midpoint of the line segment is calculated. The three-dimensional measuring apparatus according to claim 1, wherein the three-dimensional measuring apparatus is an intersection. 3. The three-dimensional measurement apparatus according to claim 1, wherein when there are two or more virtual rays, the position of the center of gravity of a plurality of intersections of combinations of the two rays is calculated as the position of the measurement object. A method for measuring the position of a measurement object from an input image,
The input image is an image captured by a camera through a mirror, and the measurement object and a predetermined feature pattern in which a position and orientation relationship from the camera is a predetermined relationship are reflected,
The relative positional relationship between the camera and the measurement object is fixed, and a plurality of images captured as variable positional relationship between the mirror and the camera are input as the input image,
About the center position of the feature pattern in the mirror space calculated based on the position of the feature pattern reflected in the input image and the focal length of the camera, and the center position of the feature pattern in the real space known from the camera,
By mirror conversion, the midpoint of the line segment connecting the center point of the real space feature pattern and the mirror space feature pattern is the origin of the mirror plane coordinates, and the vector parallel to the line segment is one coordinate axis of the mirror plane coordinates. Calculating a plane passing through the mirror plane coordinate origin and perpendicular to the coordinate axis as a mirror plane, and calculating a mirror plane coordinate represented by two coordinate axes arbitrarily set on the coordinate axis and the mirror plane;
Calculating a camera coordinate system of a mirror space obtained by mirror-transforming camera coordinates around the mirror plane;
Calculating a ray indicating the direction of the measurement object from the camera coordinates using the position of the measurement object in the input image;
The virtual camera coordinate origin as a starting point, comprising a step of calculating as a virtual ray a vector obtained by mirror-transforming the ray around the mirror plane,
Calculating a point of intersection of a plurality of virtual rays calculated based on each of a plurality of input images as a position of a measurement object. When the light rays do not intersect, the intersection of the virtual rays is calculated as a normal line composed of two light beam direction vectors, a line segment connecting two light rays parallel to the normal line is calculated, and a midpoint of the line segment is calculated. The three-dimensional measurement method according to claim 4, wherein the intersection is an intersection. 6. The three-dimensional measurement method according to claim 4, wherein when there are two or more virtual rays, the center-of-gravity position of a plurality of intersections of combinations of the two rays is calculated as the position of the measurement object. A program for causing a computer to measure the position of a measurement object from an input image,
The input image is an image captured by a camera through a mirror, and a measurement object and a predetermined feature pattern in which a position and orientation relationship from the camera is a predetermined relationship are reflected,
The relative positional relationship between the camera and the measurement object is fixed, and a plurality of images captured as variable positional relationship between the mirror and the camera are input as the input image,
About the center position of the feature pattern in the mirror space calculated based on the position of the feature pattern reflected in the input image and the focal length of the camera, and the center position of the feature pattern in real space known from the camera,
By mirror conversion, the midpoint of the line segment connecting the center point of the real space feature pattern and the mirror space feature pattern is the origin of the mirror plane coordinates, and the vector parallel to the line segment is one coordinate axis of the mirror plane coordinates. Calculating a plane passing through the mirror plane coordinate origin and perpendicular to the coordinate axis as a mirror plane, and calculating a mirror plane coordinate represented by two coordinate axes arbitrarily set on the coordinate axis and the mirror plane;
Calculating a camera coordinate system of a mirror space obtained by mirror-transforming camera coordinates around the mirror plane;
Calculating a ray indicating the direction of the measurement object from the camera coordinates using the position of the measurement object in the input image;
The virtual camera coordinate origin as a starting point, comprising a step of calculating as a virtual ray a vector obtained by mirror-transforming the ray around the mirror plane,
Calculating the intersection of a plurality of virtual rays calculated based on each of the plurality of input images as the position of the measurement object;
A three-dimensional measurement program for causing the computer to execute. When the light rays do not intersect, the intersection of the virtual rays is calculated as a normal line composed of two light beam direction vectors, a line segment connecting two light rays parallel to the normal line is calculated, and a midpoint of the line segment is calculated. The three-dimensional measurement program according to claim 7, wherein the three-dimensional measurement program is an intersection. 9. The three-dimensional measurement program according to claim 7, wherein when there are two or more virtual rays, the center-of-gravity position of a plurality of intersections of combinations of the two rays is calculated as the position of the measurement object.