Displacement Measuring Device

Abstract

To provide a displacement measurement device and a displacement measurement method that can measure displacement of a plurality of markers, that is, a plurality of measurement points at a low cost.SOLUTION: A marker image creation unit 30 extracts, for a panorama image 25#1 obtained through imaging at a time point #1 and a panorama image 25#2 obtained through imaging at a time point #2, a plurality of known marker areas where a plurality of markers are present to create a plurality of marker images R#1, M1#1 to Mn#1, R#2, M1#2 to Mn#2. A marker image analysis unit 28a calculates the amount of displacement D1 (x, y) to Dn (x, y) for each of the plurality of markers generated between the time point #1 and the time point #2 based on the plurality of marker images R#1, M1#1 to Mn#1 created from the panorama image 25#1, and the plurality of marker images R#2, M1#2 to Mn#2 created from the panorama image 25#2.SELECTED DRAWING: Figure 5

Description

[Technical Field]

[0001] The present invention relates to a displacement measuring device and a displacement measuring method. [Background technology]

[0002] Patent Document 1 shows a method for measuring dimensions without providing shape data of the target space, based on omnidirectional photographs taken from a single viewpoint through a limited opening such as an inspection hatch. Specifically, omnidirectional photographs are taken using a panoramic photography device, leveling is performed using information on vertical or horizontal lines in the target space, the results are projected onto a regular hexahedron and synthesized as a cubic panoramic image, and three-dimensional coordinate measurement is performed using the generated cubic panoramic image and height information from the camera.

[0003] Patent Document 2 discloses a method that can reduce unnecessary measurements compared to measuring the distance to a subject once for each of all the images required for one panoramic image capture. Specifically, directional light is emitted to a subject within a specific image capture range among multiple image capture ranges in panoramic image capture, and the distance to the subject is measured by receiving the reflected light, and if the measurement is successful, measurements targeting the subject within the multiple image capture ranges are prohibited.

[0004] Patent Document 3 discloses a method for inputting time-series image data obtained by photographing a predetermined pattern attached to a columnar structure, determining the displacement occurring in the columnar structure from the time-series image data, determining the natural frequency of the columnar structure from the displacement, and judging the state of the columnar structure based on the natural frequency. When determining the displacement occurring in the columnar structure, a digital image correlation method or a moire fringe phase analysis method is used.

[0005] Patent Document 4 discloses a method for reducing errors due to the tilt of the target surface or the measurement direction when measuring the displacement of a measurement point on the target surface using the sampling moiré method. Patent Document 5 discloses a method for measuring the in-plane displacement and out-of-plane displacement of an object using the sampling moiré method based on an image obtained from a single camera. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Japanese Patent Application Laid-Open No. 2015-125002 [Patent Document 2] International Publication No. 2017 / 149850 [Patent Document 3] Japanese Patent Application Publication No. 2018-141663 [Patent Document 4] Japanese Patent Application Publication No. 2019-11984 [Patent Document 5] International Publication No. 2017 / 029905 Summary of the Invention [Problem to be solved by the invention]

[0007] In recent years, technology for measuring the displacement of an object based on images captured by an imaging device has been developed. This technology involves capturing an image of a marker attached to an object and then performing various image processing on the captured image to calculate the displacement of the marker and, ultimately, the object. Compared to using dedicated surveying equipment such as a total station, this technology can reduce equipment costs and improve work efficiency through automation. Furthermore, various advantages are achieved, such as the ability to record measurement results not only as numerical values ​​but also in the form of images, the ability to perform continuous measurements using an infrared camera, and the ability for the imaging device to double as a surveillance camera.

[0008] For example, at a construction site or the like, it may be necessary to measure displacement at multiple measurement points on one or multiple objects. In this case, it is sufficient to capture images of multiple markers attached to the multiple measurement points. However, capturing images of multiple markers generally requires a long imaging distance. In this case, there is a risk that the angle of view will become narrower or the resolution of the captured image will decrease. To address this issue, a method of capturing images of multiple markers by allocating them to multiple imaging devices can be considered. However, this method may result in increased costs.

[0009] The present invention has been made in consideration of the above, and one of its objects is to provide a displacement measurement device and a displacement measurement method that can measure the displacement of multiple markers, and ultimately multiple measurement points, at low cost. [Means for solving the problem]

[0010] Among the inventions disclosed in this application, the outline of representative inventions will be briefly explained as follows.

[0011] A displacement measuring device according to a representative embodiment of the present invention includes an imaging device that captures images of markers and a displacement measuring instrument that measures the displacement of the markers based on images captured by the imaging device. The imaging device captures images of multiple markers attached to one or more objects and creates a panoramic image including the multiple markers in a single image by combining the captured images. The displacement measuring instrument includes a marker image creation unit and a marker image analysis unit. The marker image creation unit creates an image of the multiple markers by extracting known marker regions containing the multiple markers from a first panoramic image obtained by imaging at a first time point and a second panoramic image obtained by imaging at a second time point. The marker image analysis unit calculates the amount of displacement for each of the multiple markers that occurred between the first and second time points based on the multiple marker images created from the first panoramic image and the multiple marker images created from the second panoramic image. [Effects of the Invention]

[0012] To briefly explain the effect obtained by a representative invention among the inventions disclosed in this application, it becomes possible to measure the displacement of a plurality of markers, and therefore a plurality of measurement points, at low cost. [Brief explanation of the drawings]

[0013] [Figure 1] 1 is a schematic diagram showing an example of the configuration of a displacement measuring system according to a first embodiment of the present invention. [Figure 2] FIG. 2 is a schematic diagram showing an example of the configuration of a marker in FIG. [Figure 3] FIG. 2 is a block diagram showing a schematic configuration example of the displacement measuring device in FIG. [Figure 4] FIG. 3 is a schematic diagram showing an example of a panoramic image captured by the imaging device. [Figure 5] FIG. 4 is a block diagram showing an example of a schematic configuration of a main part of the displacement measuring instrument shown in FIG. 3. [Figure 6] FIG. 6 is a block diagram showing an example of the configuration of a sampling moiré unit in FIG. 5. [Figure 7] 7 is a schematic diagram illustrating an example of processing content of a phase detection unit in FIG. 6. FIG. [Figure 8] 10 is a schematic diagram showing an example of the configuration of a marker in FIG. 1 in a displacement measuring device according to a second embodiment. FIG. [Figure 9] FIG. 4 is a block diagram showing a schematic configuration example of a main part of the displacement measuring device in FIG. 3 in the displacement measuring device according to the second embodiment. [Figure 10] 10 is a block diagram showing an example of the configuration of a phase-only correlation unit in FIG. 9. FIG. [Figure 11] 10 is a schematic diagram showing an example of the configuration of a marker in FIG. 1 in a displacement measuring device according to a third embodiment. FIG. [Figure 12] FIG. 4 is a block diagram showing a schematic configuration example of a main part of the displacement measuring device in FIG. 3 in the displacement measuring device according to the third embodiment. [Figure 13] 13 is a conceptual diagram illustrating an example of processing details of a displacement amount calculation unit in FIG. 12. FIG. DETAILED DESCRIPTION OF THE INVENTION

[0014] Hereinafter, each embodiment of the present invention will be described with reference to the drawings. Note that the disclosure is merely an example, and any appropriate modifications that a person skilled in the art can easily conceive while maintaining the gist of the invention are naturally included within the scope of the present invention. Furthermore, in order to clarify the explanation, the drawings may show the width, thickness, shape, etc. of each part schematically compared to the actual embodiment, but these are merely examples and do not limit the interpretation of the present invention.

[0015] Furthermore, in this specification and each drawing, elements similar to those previously described with respect to the previous drawings are given the same reference numerals, and detailed descriptions thereof may be omitted as appropriate.

[0016] (Embodiment 1) <Outline of the displacement measurement system> FIG. 1 is a schematic diagram showing an example of the configuration of a displacement measurement system according to a first embodiment of the present invention. FIG. 2 is a schematic diagram showing an example of the configuration of the markers in FIG. 1. The displacement measurement system shown in FIG. 1 includes multiple markers 1r, 1m[1] to 1m[n] attached to one or multiple objects 3[0] to 3[n], and a displacement measurement device 2 including an imaging device. In this specification, the multiple markers 1r, 1m[1] to 1m[n] are collectively referred to as markers 1. The objects 3[0] to 3[n] are, for example, structures installed on the ground at a construction site such as a shaft construction site, or the ground itself.

[0017] The displacement measuring device 2 captures an image of the marker 1 using an imaging device, and measures the displacement of the marker 1, and therefore the displacement of the structure, ground, etc., based on the captured image. This allows for continuous monitoring of the displacement status of the structure, ground, etc., and makes it possible to detect early signs of an accident, such as the collapse of a structure or a landslide. As a result, accidents can be prevented before they occur, and the safety of workers can be ensured.

[0018] Marker 1r is a reference marker attached to a measurement point treated as a fixed point. On the other hand, markers 1m[1] to 1m[n] other than reference marker 1r are measurement markers attached to actual measurement points. For example, displacement may occur not in marker 1 but in the installation angle of the imaging device in displacement measurement device 2. By providing reference marker 1r, it becomes possible to detect such displacement of the imaging device itself. However, if it can be guaranteed that no displacement of the imaging device itself occurs, multiple markers 1r, 1m[1] to 1m[n] may all be treated as measurement markers.

[0019] Here, the imaging device in the displacement measuring device 2 is a panoramic camera capable of panoramic photography. As a result, the imaging device captures multiple markers 1r, 1m[1] to 1m[n] and creates a panoramic image that includes the multiple markers 1r, 1m[1] to 1m[n] in a single image. Generally, a panoramic camera captures multiple imaging areas while switching between imaging areas so that some areas overlap, and then creates a single panoramic image by stitching the multiple captured images obtained from the multiple imaging areas together. As a result, the panoramic image appears as if it were captured over a wide angle of view, for example, exceeding 180°, without reducing resolution.

[0020] In the specification, as shown in Fig. 1, the optical axis direction of the imaging device in the displacement measuring device 2 is defined as the Z axis, one direction in the plane direction perpendicular to the Z axis, here the horizontal direction, is defined as the X axis, and the direction perpendicular to the one direction, here the vertical direction, is defined as the Y axis. The multiple markers 1r, 1m[1] to 1m[n] are attached so that the XY plane is imaged. For example, a pattern as shown in Fig. 2 is printed on each of the XY planes of the multiple markers 1r, 1m[1] to 1m[n].

[0021] A periodic pattern is printed on the marker 1A shown in FIG. 2. By using the periodic pattern, the displacement of the marker can be measured using a sampling moiré method, which will be described later. In this example, the periodic pattern is a lattice pattern, in which black level squares are arranged at equal intervals in the X-axis direction and the Y-axis direction, sandwiching white level squares. The pitch of the black level or white level squares in the X-axis direction is Wx [mm], and the pitch in the Y-axis direction is Wy [mm], and the pitches Wx and Wy may be, for example, several mm to several tens of mm.

[0022] Furthermore, the grid pattern shown in FIG. 2 is essentially equivalent to a stripe pattern aligned in the X-axis direction or the Y-axis direction. That is, by performing image processing on the grid pattern, specifically averaging processing along the Y-axis direction, it can be converted into a stripe pattern aligned in the X-axis direction. Similarly, by performing image processing on the grid pattern, specifically averaging processing along the X-axis direction, it can be converted into a stripe pattern aligned in the Y-axis direction. Note that the periodic pattern is not limited to a grid pattern, and may be such a stripe pattern.

[0023] <Outline of displacement measurement device> FIG. 3 is a block diagram showing a schematic configuration example of the displacement measuring device in FIG. 1. The displacement measuring device 2 shown in FIG. 3 includes an imaging device 10, which is a panoramic camera, and a displacement measuring instrument 20, which is realized by an information processing device such as a PC (Personal Computer) or a dedicated image processing device. However, the imaging device 10 and the displacement measuring instrument 20 may be implemented in the same device, for example, in the form of an information processing device with a panoramic camera. As described above, the imaging device 10 captures images of multiple markers 1 and creates a panoramic image including the multiple markers 1 in a single image. The displacement measuring instrument 20 measures the amount of displacement for each of the multiple markers 1, and therefore for each of the multiple measurement points, based on the panoramic image created by the imaging device 10.

[0024] The imaging device 10 includes a lens 11, an image sensor 12, a computing unit 13, an internal memory 14, a communication interface 15, and a panoramic mechanism 16. The computing unit 13, the internal memory 14, and the communication interface 15 are connected to one another via a bus. The computing unit 13, the internal memory 14, and the communication interface 15 may be implemented in, for example, a single microcontroller.

[0025] The lens 11 focuses light from the imaging area onto the image sensor 12. The image sensor 12 is typically a CMOS (Complementary Metal Oxide Semiconductor) image sensor or a CCD (Charge Coupled Device) image sensor, and includes a plurality of pixels arranged in an array. Each pixel of the image sensor 12 generates an electrical signal corresponding to the amount of light focused by the lens 11. The image sensor 12 transmits the electrical signal generated by each pixel to the calculator 13.

[0026] The internal memory 14 is a non-volatile memory such as a flash memory, and corresponds to a built-in memory in a microcontroller or an external memory such as a memory card. The panoramic mechanism 16 switches the imaging area by, for example, mechanically moving the lens 11 or the imaging device 10 itself in response to an instruction from the computing unit 13. Note that the type of the panoramic camera is not limited to such a mechanically moving type, and various known types may be used, including, for example, a type that includes multiple lenses.

[0027] The computing unit 13 includes a processor 13a, such as a central processing unit (CPU), a graphics processing unit (GPU), or a digital signal processor (DSP), and a random access memory (RAM) 13b. The processor 13a executes various processes required to create a panoramic image, for example, by executing a program loaded from the internal memory 14 to the RAM 13b. In detail, the processor 13a creates an image for each imaging area based on an electrical signal from the image sensor 12 while switching the imaging area via the panorama mechanism 16. Furthermore, the processor 13a stitches together the images for each imaging area to create a single panoramic image, and stores the panoramic image in the internal memory 14.

[0028] The communication interface 15 transmits and receives data to and from the displacement measuring instrument 20, specifically, the communication interface 21 therein. As one of the transmissions, the communication interface 15 transmits a panoramic image stored in the internal memory 14 to the displacement measuring instrument 20. The communication interface 15 and the communication interface 21 are connected by wire or wirelessly. In this case, for example, a connection via an external network such as the Internet may be used.

[0029] When using an external network, it is useful to install, for example, the imaging device 10 equipped with a communication interface 15 for wireless communication permanently at the construction site, and to install the displacement measuring instrument 20 on an in-house server device of the construction company. In this case, the imaging device 10 sequentially transmits the created panoramic images to the in-house server device via the external network, and the in-house server device can perform displacement measurement based on the panoramic images.

[0030] The displacement measuring instrument 20 includes a computing unit 22, an internal memory 23, and a communication interface 21. The computing unit 22, the internal memory 23, and the communication interface 21 are connected to one another via a bus. For example, if the displacement measuring instrument 20 is configured using a dedicated image processing device or the like, the computing unit 22, the internal memory 23, and the communication interface 21 may be implemented in a single microcontroller. The internal memory 23 is, for example, a non-volatile memory such as a flash memory or a hard disk drive. The communication interface 21 receives a panoramic image from, for example, the communication interface 15 of the imaging device 10 and stores it in the internal memory 23.

[0031] The calculator 22 includes a processor 22a such as a CPU, a GPU, or a DSP, and a RAM 22b. The calculator 22 calculates the amount of displacement for each of the multiple markers 1, for example, by performing predetermined image processing on a panoramic image stored in the internal memory 23. At this time, the processor 22a calculates the amount of displacement by, for example, executing a displacement measurement program loaded from the internal memory 23 to the RAM 22b. Note that the calculator 22 is not limited to the processor 22a, and may be partially or entirely configured with hardware such as an FPGA (Field Programmable Gate Array) or an ASIC (Application Specific Integrated Circuit). In other words, the calculator 22 may be configured as appropriate using software, hardware, or a combination thereof. The same applies to the calculator 13 in the imaging device 10.

[0032] <Outline of displacement measuring instrument> Fig. 4 is a schematic diagram showing an example of a panoramic image captured by the imaging device in Fig. 3. The panoramic image 25 shown in Fig. 4 includes multiple markers 1, i.e., a reference marker 1r and measurement markers 1m[1] to 1m[n], in one image. The panoramic image 25 is created by, for example, combining captured images 26[0] to 26[n] of multiple imaging regions that are set so that some regions overlap.

[0033] Fig. 5 is a block diagram showing a schematic configuration example of the main parts of the displacement measuring instrument in Fig. 3. The displacement measuring instrument 20 shown in Fig. 5 includes a marker image creation unit 30 and a marker image analysis unit 28a. These units are realized, for example, by the processor 22a executing a displacement measurement program. Furthermore, the internal memory 23 of the displacement measuring instrument 20 stores panoramic images 25 at each time point, including a panoramic image 25#1 obtained by imaging at time point #1 and a panoramic image 25#2 obtained by imaging at a subsequent time point #2.

[0034] The marker image creation unit 30 creates multiple marker images by extracting known marker regions in which multiple markers 1 exist from multiple panoramic images 25 stored in the internal memory 23. That is, the marker regions in which markers 1 exist within the panoramic images 25 are fixedly determined in advance based on the positional relationships at the stage when the displacement measurement system shown in Fig. 1 is constructed. In the example shown in Fig. 4, for each of the markers 1r, 1m[1] to 1m[n], a pixel range slightly inside the outer frame is fixedly determined as the marker region, and a marker image 27 is created by extracting an image of this marker region.

[0035] The marker image creation unit 30 stores the created marker image 27 in, for example, RAM 22b. The created marker image 27 includes a reference marker image R#1 and measurement marker images M1#1 to Mn#1 at time point #1, and a reference marker image R#2 and measurement marker images M1#2 to Mn#2 at time point #2. For example, the reference marker image R#1 and the measurement marker images M1#1 to Mn#1 are created by extracting the marker regions of the reference marker 1r and the measurement markers 1m[1] to 1m[n], respectively, from the panoramic image 25#1 at time point #1.

[0036] In this specification, reference marker images R#1 and R#2 are collectively referred to as reference marker image R or simply as marker image R. Furthermore, measurement marker images M1#1 and M1#2 are collectively referred to as measurement marker image M1 or simply as marker image M1. Similarly, measurement marker images Mn#1 and Mn#2 are collectively referred to as measurement marker image Mn or simply as marker image Mn.

[0037] Marker image analysis unit 28a calculates the amount of displacement for each of multiple markers 1 that occurred between time point #1 and time point #2, based on multiple marker images R#1, M1#1 to Mn#1 created from panoramic image 25#1 and multiple marker images R#2, M1#2 to Mn#2 created from panoramic image 25#2. Specifically, marker image analysis unit 28a includes sampling moiré unit 31 and displacement amount calculation unit 32.

[0038] The sampling moiré unit 31 detects the phase of the moiré fringes, designated PH#1 here, for each of the plurality of marker images R#1, M1#1 to Mn#1 created from the panoramic image 25#1, using the sampling moiré method. Similarly, the sampling moiré unit 31 detects the phase of the moiré fringes, designated PH#2 here, for each of the plurality of marker images R#2, M1#2 to Mn#2 created from the panoramic image 25#2. Then, based on the difference between the detected phase PH#1 and phase PH#2, the sampling moiré unit 31 calculates the phase difference of the moiré fringes for each of the plurality of marker images R, M1 to Mn that occurred between time point #1 and time point #2.

[0039] That is, the sampling moiré unit 31 calculates the phase difference ΔPHr(x,y) occurring in the reference marker image R and the phase differences ΔPHm1(x,y) to ΔPHmn(x,y) occurring in the measurement marker images M1 to Mn. Each of the phase differences ΔPHr(x,y) and ΔPHm1(x,y) to ΔPHmn(x,y) includes a phase difference ΔPH(x) in the X-axis direction and a phase difference ΔPH(y) in the Y-axis direction.

[0040] The displacement amount calculation unit 32 calculates the displacement amount for each marker 1, for example, the displacement amounts D1(x,y) to Dn(x,y) [mm] for each measurement marker 1m[1] to 1m[n], based on the phase differences ΔPHr(x,y), ΔPHm1(x,y) to ΔPHmn(x,y) [rad] of the moiré fringes for each marker image R, M1 to Mn calculated by the sampling moiré unit 31. Each of the displacement amounts D1(x,y) to Dn(x,y) includes a displacement amount D(x) in the X-axis direction and a displacement amount D(y) in the Y-axis direction.

[0041] Specifically, the phase difference ΔPH(x) [rad] in the X-axis direction and the phase difference ΔPH(y) [rad] in the Y-axis direction from the sampling moiré unit 31, and the displacement amount D(x) [mm] in the X-axis direction and the displacement amount D(y) [mm] in the Y-axis direction calculated by the displacement amount calculation unit 32 have the relationship shown in equations (1) and (2). In equations (1) and (2), Wx [mm] and Wy [mm] are the pitches on the marker 1A shown in FIG. 2, respectively. The displacement amount calculation unit 32 calculates the displacement amounts D1(x,y) to Dn(x,y) for each of the measurement markers 1m[1] to 1m[n] using equations (1) and (2). D(x)=(ΔPH(x) / 2π)×Wx …(1) D(y)=(ΔPH(y) / 2π)×Wy …(2)

[0042] However, at this time, the displacement amount calculation unit 32 calculates the displacement amounts D1(x,y) to Dn(x,y) of each of the measurement markers 1m[1] to 1m[n] as a difference value from the displacement amount of the reference marker 1r. In detail, the displacement amount calculation unit 32 regards the difference value "ΔPHm1(x,y)-ΔPHr(x,y)" between the phase difference ΔPHm1(x,y) occurring in the measurement marker 1m[1] and the phase difference ΔPHr(x,y) occurring in the reference marker 1r as the phase difference occurring in the measurement marker 1m[1]. Then, the displacement amount calculation unit 32 calculates the displacement amount D1(x,y) of the measurement marker 1m[1] by substituting the regarded phase difference into equations (1) and (2).

[0043] Similarly, the displacement amount calculation unit 32 regards the difference value between the phase difference ΔPHmn(x,y) occurring in the measurement marker 1m[n] and the phase difference ΔPHr(x,y) occurring in the reference marker 1r as the phase difference occurring in the measurement marker 1m[n], and calculates the displacement amount Dn(x,y) of the measurement marker 1m[n]. In this way, by calculating the phase difference, and therefore the displacement amount, of the measurement markers 1m[1] to 1m[n] as the difference value from the phase difference, and therefore the displacement amount, of the reference marker 1r, it is possible to detect the displacement of the imaging device 10, as described in FIG. 1, and it becomes possible to measure the displacement of each measurement marker while reflecting the displacement of the imaging device 10.

[0044] <Details of the sampling moire section> FIG. 6 is a block diagram showing an example of the configuration of the sampling moiré unit in FIG. 5. FIG. 7 is a schematic diagram illustrating an example of the processing content of the phase detection unit in FIG. 6. The sampling moiré unit 31 shown in FIG. 6 includes a phase detection unit 35 and a phase difference calculation unit 36. The phase detection unit 35 detects the phase PH(x,y)#1 of the moiré fringes for marker image 27#1 at time point #1 using the sampling moiré method, and similarly detects the phase PH(x,y)#2 of the moiré fringes for marker image 27#2 at time point #2. Marker image 27#1 corresponds to one of reference marker image R#1 and measurement marker images M1#1 to Mn#1 at time point #1, and marker image 27#2 corresponds to one of reference marker image R#2 and measurement marker images M1#2 to Mn#2 at time point #2.

[0045] Here, each of the phases PH(x,y)#1 and PH(x,y)#2 includes a phase PH(x) in the X-axis direction and a phase PH(y) in the Y-axis direction. The phase PH(x) in the X-axis direction is obtained from a periodic pattern aligned in the X-axis direction, and the phase PH(y) in the Y-axis direction is obtained from a periodic pattern aligned in the Y-axis direction. As described with reference to FIG. 2, when detecting the phase PH(x) in the X-axis direction, the phase detection unit 35 converts the grid pattern represented by the marker image 27 into a stripe pattern aligned in the X-axis direction as a preprocessing. Similarly, when detecting the phase PH(y) in the Y-axis direction, the phase detection unit 35 converts the grid pattern represented by the marker image 27 into a stripe pattern aligned in the Y-axis direction as a preprocessing.

[0046] Fig. 7 shows the principle of the sampling moiré method used in the phase detection unit 35. In Fig. 7, an imaging device 10 having a plurality of pixels P arranged at a pitch p captures an image of a marker 1A to create a marker image 27 including a periodic pattern. The phase detection unit 35 detects the phase of the moiré fringes by performing the following processing based on the sampling moiré method on this periodic pattern.

[0047] First, the phase detection unit 35 samples pixels P at predetermined intervals, typically every four pixels, of the periodic pattern in the marker image 27 to create a sampled image. At this time, the phase detection unit 35 shifts the positions of the pixels to be sampled in order to create four sampled images 40[0] to 40[3].

[0048] Next, the phase detection unit 35 performs interpolation on each of the four sampling images 40[0] to 40[3] to create four moiré images 41[0] to 41[3] containing moiré fringes. Next, the phase detection unit 35 calculates equation (3) for each of the multiple pixels P to determine the phase of the moiré fringes contained in the moiré image 41[0], more specifically, the phase PH for each pixel P in the moiré fringe luminance distribution 42. In equation (3), I0, I1, I2, and I3 are the luminance values ​​of the moiré images 41[0], 41[1], 41[2], and 41[3] at each pixel P, respectively. tan(PH)=-(I3-I1) / (I2-I0) …(3)

[0049] Here, the luminance value In of each pixel P in a moiré image 41[n] (n=0, 1, 2, 3) can generally be expressed by equation (4) using luminance amplitude A0, phase PH, and background luminance B0. In equation (4), if the unknowns A0 and B0 are known, it is possible to calculate the phase PH. Therefore, in the sampling moiré method, for example, as shown in FIG. 7, four moiré images 41[0] to 41[3] are created, each with a phase shift of π / 2, so that four luminance values ​​I0 to I3 can be obtained for each pixel P. Once the four luminance values ​​I0 to I3 are obtained, four simultaneous equations can be created based on equation (4). Equation (3) is an equation used to calculate the phase PH from these four simultaneous equations. In=A0×cos(PH+(n×π / 2))+B0 …(4)

[0050] Using this sampling moiré method, the phase detection unit 35 detects a phase PH(x,y)#1 for each marker image 27#1 at time #1 for each of multiple pixels P, and detects a phase PH(x,y)#2 for each marker image 27#2 at time #2. As shown in FIG. 7, a method of creating multiple grid images (here, moiré images) with sequentially shifted phases and calculating the phase PH of the grid (here, moiré fringes) using equation (3) or the like is also called a phase shifting method. The sampling moiré method utilizes this phase shifting method and applies a moiré image created by sampling pixels P as the grid image.

[0051] Returning to FIG. 6, the phase difference calculation unit 36 ​​includes an average value calculation unit 37. The phase difference calculation unit 36 ​​receives an input from the phase detection unit 35 and calculates the phase difference between a phase PH(x,y)#1 at time point #1 and a phase PH(x,y)#2 at time point #2. In detail, the phase difference calculation unit 36 ​​calculates such a phase difference for each of a plurality of pixels P using equation (3). The average value calculation unit 37 calculates the average value of the phase differences obtained from the plurality of pixels P and outputs the calculated phase difference ΔPH(x,y) to the displacement amount calculation unit 32 shown in FIG. 5.

[0052] The sampling moiré method is generally used to measure the in-plane displacement of the area where the marker 1 is attached, in other words, the deformation state of an object, based on the phase difference for each pixel P. On the other hand, for example, at a construction site such as a shaft construction site, when measuring the displacement of a building or the ground, information on the in-plane displacement of the marker 1 is not particularly required. Instead, information on the overall displacement of the marker 1, and ultimately, information on the movement of the object itself, is often required. To measure the displacement of the entire marker 1 in this manner, in this example, an average value is calculated using an average value calculation unit 37. Furthermore, the lower the resolution of the marker image 27, the lower the accuracy and resolution of the displacement measurement. Therefore, the marker image 27 must have a relatively high resolution. For this reason, it is useful to create a panoramic image 25 as shown in FIG. 4.

[0053] <Major Effects of the First Embodiment> As described above, by using the method of the first embodiment, it is typically possible to measure the displacement of multiple markers 1, and therefore multiple measurement points, at low cost. In detail, in the method of the first embodiment, the imaging device 10 creates a panoramic image 25 including multiple markers 1 in a single image, and the displacement measuring instrument 20 can measure the displacement of each of the multiple markers 1 based on multiple marker images 27 with sufficient resolution extracted from the panoramic image 25. As a result, there is no need to provide multiple imaging devices to obtain sufficient resolution, and high-resolution or high-precision displacement measurement can be performed by providing a single imaging device 10.

[0054] Furthermore, in the method of the first embodiment, a reference marker 1r is provided, and the displacement amount of each of the measurement markers 1m[1] to 1m[n] is calculated as a difference value from the displacement amount of the reference marker 1r. As a result, it becomes possible to measure the displacement of each of the measurement markers 1m[1] to 1m[n] while reflecting the displacement of the imaging device 10. In this case, the reference marker image R and the measurement marker images M1 to Mn are not captured by different imaging devices, but are captured by panoramic photography using a single imaging device 10, that is, are captured under substantially the same conditions, so that it is unlikely that the displacement of the imaging device 10 will be erroneously determined.

[0055] (Embodiment 2) <Outline of displacement measuring instrument> FIG. 8 is a schematic diagram showing an example of the configuration of the marker in FIG. 1 in the displacement measuring device according to the second embodiment. A geometric pattern is inscribed on the marker 1B shown in FIG. 8. By using the geometric pattern, it is possible to measure the displacement of the marker using a phase-only correlation method, which will be described later, or the like. In this example, the geometric pattern is six circles arranged at 60° intervals. However, the geometric pattern is not limited to this, and various commonly known patterns may be used, and in particular, any pattern that does not contain periodic components in the X-axis and Y-axis directions may be used.

[0056] 9 is a block diagram showing a schematic configuration example of the main parts of the displacement measuring instrument in FIG. 3 in a displacement measuring device according to Embodiment 2. The displacement measuring instrument 20 shown in FIG. 9 includes a marker image creation unit 30 and a marker image analysis unit 28b. As in the case of FIG. 5, the marker image creation unit 30 creates multiple marker images by extracting multiple known marker areas from panoramic images 25#1, 25#2, ... stored in internal memory 23. However, in FIG. 4, the marker images 27 of the reference marker 1r and measurement markers 1m[1] to 1m[n] included in the panoramic image 25 are shaped in such a way that the periodic pattern shown in FIG. 2 is replaced with the geometric pattern shown in FIG.

[0057] Marker image analysis unit 28b calculates the amount of displacement that occurred for each of multiple markers 1 between time point #1 and time point #2 based on multiple marker images R#1, M1#1 to Mn#1 created from panoramic image 25#1 and multiple marker images R#2, M1#2 to Mn#2 created from panoramic image 25#2, as in the case of Fig. 5. However, marker image analysis unit 28b, unlike the case of Fig. 5, includes a phase-only correlation unit 45 and a displacement amount calculation unit 46.

[0058] The phase-only correlation unit 45 calculates the correlation between the plurality of marker images R#1, M1#1 to Mn#1 created from the panoramic image 25#1 and the plurality of marker images R#2, M1#2 to Mn#2 created from the panoramic image 25#2 using the phase-only correlation method. As a result, the phase-only correlation unit 45 calculates the amount of shift for each of the plurality of marker images R, M1 to Mn that occurred between time point #1 and time point #2.

[0059] That is, the phase-only correlation unit 45 calculates the shift amount ΔSFr(x,y) that occurred in the reference marker image R and the shift amounts ΔSFm1(x,y) to ΔSFmn(x,y) that occurred in the measurement marker images M1 to Mn. Each of the shift amounts ΔSFr(x,y) and ΔSFm1(x,y) to ΔSFmn(x,y) includes a shift amount ΔSF(x) in the X-axis direction and a shift amount ΔSF(y) in the Y-axis direction.

[0060] The displacement amount calculation unit 46 calculates the displacement amount for each marker 1, for example, displacement amounts D1(x,y) to Dn(x,y) [mm] for each measurement marker 1m[1] to 1m[n], based on the shift amounts ΔSFr(x,y), ΔSFm1(x,y) to ΔSFmn(x,y) [pixels (px)] for each marker image R, M1 to Mn calculated by the phase-only correlation unit 45. Each of the displacement amounts D1(x,y) to Dn(x,y) includes a displacement amount D(x) in the X-axis direction and a displacement amount D(y) in the Y-axis direction.

[0061] Specifically, the X-axis direction shift amount ΔSF(x) [px] and the Y-axis direction shift amount ΔSF(y) [px] from the phase-only correlation unit 45 and the X-axis direction displacement amount D(x) [mm] and the Y-axis direction displacement amount D(y) [mm] calculated by the displacement amount calculation unit 46 have the relationship shown in equations (5) and (6). In equations (5) and (6), Lx [mm] and Ly [mm] are the X-axis direction length and the Y-axis direction length on the marker 1 corresponding to one pixel of the image sensor 12, and are fixedly determined based on the number of pixels of the image sensor 12, the optical magnification setting at the time of image capture, etc. The displacement amount calculation unit 46 calculates the displacement amounts D1(x,y) to Dn(x,y) for each of the measurement markers 1m[1] to 1m[n] using equations (5) and (6). D(x) = ΔSF(x) × Lx … (5) D(y) = ΔSF(y) × Ly … (6)

[0062] However, at this time, the displacement amount calculation unit 46 calculates the displacement amounts D1(x,y) to Dn(x,y) of each of the measurement markers 1m[1] to 1m[n] as a difference value from the displacement amount of the reference marker 1r, as in the case of FIG. 5. In detail, the displacement amount calculation unit 46 regards the difference value "ΔSFm1(x,y)-ΔSFr(x,y)" between the shift amount ΔSFm1(x,y) occurring in the measurement marker 1m[1] and the shift amount ΔSFr(x,y) occurring in the reference marker 1r as the shift amount occurring in the measurement marker 1m[1]. Then, the displacement amount calculation unit 46 calculates the displacement amount D1(x,y) of the measurement marker 1m[1] by substituting the regarded shift amount into equations (5) and (6). The same applies to the other measurement markers 1m[n].

[0063] <Details of the phase-only correlation section> FIG. 10 is a block diagram showing an example of the configuration of the phase-only correlation unit in FIG. 9. A method is known in which the degree of coincidence of multiple images is determined by the correlation of the frequency components of the images. When the frequency components of an image are determined, information about the shape of the image within the image is generally retained by the phase spectrum rather than the amplitude spectrum. Taking advantage of this, the phase-only correlation method normalizes the amplitude spectrum of the frequency components of the image to, for example, 1, and then determines the correlation mainly based on the phase spectrum.

[0064] 10 includes a Fourier transform unit 50, a composite function calculation unit 51, and a correlation function calculation unit 52. Image data f1(m,n) of marker image 27#1 at time point #1 and image data f2(m,n) of marker image 27#2 at time point #2 are input to Fourier transform unit 50. Marker image 27#1 corresponds to reference marker image R#1 and one of measurement marker images M1#1 to Mn#1 at time point #1, and marker image 27#2 corresponds to reference marker image R#2 and one of measurement marker images M1#2 to Mn#2 at time point #2. Here, the pixel region of marker image 27 is M×N pixels, where m is one of M integers and n is one of N integers.

[0065] The Fourier transform unit 50 calculates the Fourier transform values ​​F1(u,v) and F2(u,v) shown in equations (7) and (8) by, for example, performing a two-dimensional discrete Fourier transform on the image data f1(m,n) and f2(m,n). In equations (7) and (8), u is one of M integers, and v is one of N integers. Furthermore, A(u,v) and B(u,v) are amplitude spectra, and e jθ1(u,v) and e jθ2(u,v) is the phase spectrum. F1(u,v)=A(u,v)×e jθ1(u,v) …(7) F2(u,v)=B(u,v)×e jθ2(u,v) …(8)

[0066] The composite function calculation unit 51 calculates the composite function C12(u,v) shown in equation (9) by multiplying the phase spectrum of the Fourier transform value F1(u,v) by the complex conjugate of the phase spectrum of the Fourier transform value F2(u,v). The correlation function calculation unit 52 calculates the correlation function c12(m,n) by performing a two-dimensional inverse discrete Fourier transform on the composite function C12(u,v) of equation (9). C12(u,v)=e j(θ1(u,v)-θ2(u,v)) …(9)

[0067] Here, for example, assume that the image positions of image data f1(m,n) and image data f2(m,n) are the same. In this case, the correlation function c12(m,n) between image data f1(m,n) and image data f2(m,n) is close to a delta function with a peak value at the origin position (0,0). On the other hand, assume that image data f2(m,n) is image data in which the image position is shifted by Δm in the m direction relative to image data f1(m,n). In this case, when the correlation function c12(m,n) between image data f1(m,n) and image data f2(m,n) (= f1(m-Δm,n)) is calculated, the position of the peak value shifts by Δm in the m direction from the origin position. The same is true for the n direction.

[0068] In this way, by using the phase-only correlation unit 45, it is possible to calculate the shift amounts in the m and n directions of the marker image 27 that occurred between time #1 and time #2, i.e., the shift amounts ΔSF(x,y) in the X-axis and Y-axis directions, based on the positions where the peak values ​​occurred. The phase-only correlation unit 45 outputs the calculated shift amounts ΔSF(x,y) to the displacement amount calculation unit 46 shown in FIG. 9. Note that the lower the resolution of the marker image 27, the lower the accuracy and resolution of the displacement measurement, so the marker image 27 needs to have a relatively high resolution. For this reason, it is useful to create a panoramic image 25 such as that shown in FIG. 4.

[0069] <Major Effects of the Second Embodiment> As described above, the method of the second embodiment can also achieve the same effects as those described in the first embodiment, typically making it possible to measure the displacement of multiple markers 1, and therefore multiple measurement points, at low cost. Comparing the sampling moiré method and the phase-only correlation method, the sampling moiré method is superior in terms of resolution, while the phase-only correlation method is superior in terms of ease of image processing, cost, and the like. Therefore, for example, when high resolution is required for displacement measurement, the method of the first embodiment should be applied, and when this is not the case, the method of the second embodiment should be applied.

[0070] That is, while the resolution is in pixel units in the phase-only correlation method, the sampling moiré method effectively measures displacement in sub-pixel units by enlarging the periodic pattern shown in marker image 27 in Figure 7 to the periodic pattern shown in moiré image 41[0]. Also, while the phase-only correlation method can measure displacement using simple arithmetic processing as described in Figure 10, the sampling moiré method requires complex image processing as described in Figure 7. Furthermore, since the phase-only correlation method does not usually require high resolution, it does not require a high-performance, i.e., expensive, image sensor 12, etc., as compared to the sampling moiré method.

[0071] (Embodiment 3) <Outline of displacement measuring instrument> Fig. 11 is a schematic diagram showing an example of the configuration of the marker in Fig. 1 in the displacement measuring device according to embodiment 3. Marker 1C shown in Fig. 11 is a combination of marker 1A shown in Fig. 2 and marker 1B shown in Fig. 8. That is, marker 1C has a geometric pattern and a periodic pattern written side by side, for example, in the X-axis direction, so that they do not overlap each other. The geometric pattern is used in the phase-only correlation method, and the periodic pattern is used in the sampling moiré method.

[0072] Fig. 12 is a block diagram showing a schematic configuration example of the main parts of the displacement measuring instrument in Fig. 3 in the displacement measuring device according to embodiment 3. The displacement measuring instrument 20 shown in Fig. 12 includes a marker image creation unit 30 and a marker image analysis unit 28c. As in the case of Fig. 5, the marker image creation unit 30 creates a plurality of marker images by extracting a plurality of known marker areas from panoramic images 25#1, 25#2, ... stored in internal memory 23.

[0073] However, in FIG. 4, the marker images 27 of the reference marker 1r and the measurement markers 1m[1] to 1m[n] included in the panoramic image 25 are replaced with a combination of a geometric pattern and a periodic pattern shown in FIG. 11 instead of the periodic pattern shown in FIG. 2. When using the marker 1C shown in FIG. 11, the area of ​​the marker image 27 may expand, which usually makes it difficult to maintain resolution. On the other hand, when the panoramic image 25 is used, it is possible to sufficiently increase the resolution of both the geometric pattern and the periodic pattern. Note that the marker area is set separately for each of the geometric pattern and the periodic pattern.

[0074] 5 and 9, marker image analysis unit 28c calculates the amount of displacement that occurred for each of multiple markers 1 between time point #1 and time point #2 based on multiple marker images R#1, M1#1 to Mn#1 created from panoramic image 25#1 and multiple marker images R#2, M1#2 to Mn#2 created from panoramic image 25#2. However, unlike the cases of FIGS. 5 and 9, marker image analysis unit 28c includes sampling moiré unit 31, phase-only correlation unit 45, and displacement amount calculation unit 55.

[0075] 5 and 6, and uses a sampling moiré method to calculate the phase difference ΔPHr(x,y) occurring in the reference marker image R and the phase differences ΔPHm1(x,y) to ΔPHmn(x,y) occurring in the measurement marker images M1 to Mn. The phase-only correlation unit 45 has the same configuration as shown in FIGS. 9 and 10, and uses a phase-only correlation method to calculate the shift amount ΔSFr(x,y) occurring in the reference marker image R and the shift amounts ΔSFm1(x,y) to ΔSFmn(x,y) occurring in the measurement marker images M1 to Mn.

[0076] The sampling moiré method uses a periodic pattern, so if a displacement of the marker 1 exceeds the length of one period of the periodic pattern, i.e., if a periodic shift occurs, it becomes difficult to detect the periodic shift. On the other hand, the phase-only correlation method uses a geometric pattern, so such a periodic shift problem does not occur. Therefore, the displacement amount calculation unit 55 determines the magnitude of the periodic shift added to the phase difference ΔPH(x,y) of the moiré fringes for each of the multiple marker images 27 calculated by the sampling moiré unit 31, based on the shift amount ΔSF(x,y) for each of the multiple marker images 27 calculated by the phase-only correlation unit 45. Then, the displacement amount calculation unit 55 calculates the displacement amounts D1(x,y) to Dn(x,y) for each of the multiple markers 1 based on the phase difference ΔPH(x,y) of the moiré fringes and the magnitude of the periodic shift.

[0077] 13 is a conceptual diagram illustrating an example of the processing performed by the displacement amount calculation unit in FIG. 12. FIG. 13 shows the phase of a luminance distribution 42#1 of moiré fringes at time point #1 and the phase of a luminance distribution 42#2 of moiré fringes at time point #2, both of which are detected by the sampling moiré unit 31. The sampling moiré unit 31 calculates the phase difference ΔPH [rad] between the phase of the luminance distribution 42#1 and the phase of the luminance distribution 42#2 in the range of −π to +π. Therefore, the actual phase difference is not necessarily ΔPH+0, but may be ΔPH+2π, ΔPH+4π, or the like. The value of 0, 2π, 4π, etc. is determined based on the shift amount ΔSF(x, y) from the phase-only correlation unit 45.

[0078] As a specific example, assume that the pitch Wx of the periodic pattern in the marker 1C shown in FIG. 11 is 5 mm, the resolution using the phase-only correlation method, i.e., Lx in equation (5), is 5 mm or less, and the actual displacement is 12 mm. When the sampling moiré method is used, the displacement result is, for example, 2 mm, 7 mm, 12 mm, 17 mm, etc. On the other hand, when the phase-only correlation method is used, the displacement result is, for example, within the range of 10 mm to 15 mm. The displacement amount calculation unit 55 can calculate the actual displacement of 12 mm based on the overlapping portion of these results.

[0079] In this way, the displacement amount calculation unit 55 calculates the actual displacement amount of the reference marker 1r and the actual displacement amount of each of the measurement markers 1m[1] to 1m[n]. Furthermore, as in the case of Fig. 5, the displacement amount calculation unit 55 calculates the correct displacement amounts D1(x,y) to Dn(x,y) for each of the measurement markers 1m[1] to 1m[n] based on the difference between the actual displacement amount of each of the measurement markers 1m[1] to 1m[n] and the actual displacement amount of the reference marker 1r.

[0080] <Major Effects of the Third Embodiment> As described above, by using the method of embodiment 3, it is possible to obtain the same effects as those described in embodiments 1 and 2, typically making it possible to measure the displacement of multiple markers 1, and therefore multiple measurement points, at low cost. Furthermore, the magnitude of the periodic shift that occurs in the sampling moiré method can be detected using the phase-only correlation method, making it possible to achieve high-resolution measurements based on the sampling moiré method over a wide measurement range.

[0081] The invention made by the inventor has been specifically described above based on an embodiment, but the present invention is not limited to the above embodiment and can be modified in various ways without departing from the gist of the invention. [Explanation of symbols]

[0082] 1, 1A to 1C... marker, 1r... reference marker, 1m[1] to 1m[n]... measurement marker, 2... displacement measurement device, 3[0] to 3[n]... object, 10... imaging device, 20... displacement measuring instrument, 25... panoramic image, 26[0] to 26[n]... captured image, 27... marker image, 28a to 28c... marker image analysis unit, 30... marker image creation unit, 31... sampling moire unit, 32, 46, 55... displacement amount calculation unit, 45... phase-only correlation unit, R... reference marker image, M1 to Mn... measurement marker image

Claims

1. An imaging device for capturing an image of a marker; a displacement measuring instrument that measures the displacement of the marker based on the image captured by the imaging device; A displacement measuring device having the imaging device captures images of a plurality of markers attached to one or a plurality of objects, and synthesizes the captured images to create a panoramic image including the plurality of markers in a single image; The displacement measuring instrument is a marker image creation unit that creates a plurality of marker images by extracting a plurality of known marker regions in which the plurality of markers exist from a first panoramic image obtained by imaging at a first time point and a second panoramic image obtained by imaging at a second time point; a marker image analysis unit that calculates a displacement amount for each of the plurality of markers that occurred between the first time point and the second time point based on the plurality of marker images created from the first panoramic image and the plurality of marker images created from the second panoramic image; Equipped with a periodic pattern is marked on each of the plurality of markers; the marker image analysis unit detects a first phase of Moiré fringes for each of the plurality of marker images created from the first panoramic image using a sampling Moiré method, detects a second phase of the Moiré fringes for each of the plurality of marker images created from the second panoramic image using the sampling Moiré method, and calculates a phase difference of the Moiré fringes for each of the plurality of marker images that occurred between the first time point and the second time point based on a difference between the first phase and the second phase. Displacement measuring device.

2. An imaging device for imaging a marker; a displacement measuring instrument that measures the displacement of the marker based on the image captured by the imaging device; A displacement measuring device having the imaging device captures images of a plurality of markers attached to one or a plurality of objects, and synthesizes the captured images to create a panoramic image including the plurality of markers in a single image; The displacement measuring instrument is a marker image creation unit that creates a plurality of marker images by extracting a plurality of known marker regions in which the plurality of markers exist from a first panoramic image obtained by imaging at a first time point and a second panoramic image obtained by imaging at a second time point; a marker image analysis unit that calculates a displacement amount for each of the plurality of markers that occurred between the first time point and the second time point based on the plurality of marker images created from the first panoramic image and the plurality of marker images created from the second panoramic image; Equipped with Each of the plurality of markers has a geometric pattern printed thereon; the marker image analysis unit calculates correlations between the plurality of marker images created from the first panoramic image and the plurality of marker images created from the second panoramic image using a phase-only correlation method, thereby calculating a shift amount for each of the plurality of marker images that occurred between the first time point and the second time point. Displacement measuring device.

3. An imaging device that captures an image of a marker; a displacement measuring instrument that measures the displacement of the marker based on the image captured by the imaging device; A displacement measuring device having the imaging device captures images of a plurality of markers attached to one or a plurality of objects, and synthesizes the captured images to create a panoramic image including the plurality of markers in a single image; The displacement measuring instrument is a marker image creation unit that creates a plurality of marker images by extracting a plurality of known marker regions in which the plurality of markers exist from a first panoramic image obtained by imaging at a first time point and a second panoramic image obtained by imaging at a second time point; a marker image analysis unit that calculates a displacement amount for each of the plurality of markers that occurred between the first time point and the second time point based on the plurality of marker images created from the first panoramic image and the plurality of marker images created from the second panoramic image; Equipped with a periodic pattern and a geometric pattern are marked on each of the plurality of markers; The marker image analysis unit a sampling moiré unit that detects a first phase of moiré fringes for each of the plurality of marker images created from the first panoramic image using a sampling moiré method for the periodic pattern, detects a second phase of the moiré fringes for each of the plurality of marker images created from the second panoramic image using the sampling moiré method, and calculates a phase difference of the moiré fringes for each of the plurality of marker images that occurred between the first time point and the second time point using a difference between the first phase and the second phase; a phase-only correlation unit that calculates correlations between the plurality of marker images created from the first panoramic image and the plurality of marker images created from the second panoramic image using a phase-only correlation method, for the geometric pattern, to calculate a shift amount for each of the plurality of marker images that occurred between the first time point and the second time point; a displacement amount calculation unit that determines the magnitude of a periodic shift added to the phase difference of the moiré fringes for each of the plurality of marker images calculated by the sampling moiré unit based on the shift amount for each of the plurality of marker images calculated by the phase-only correlation unit, and calculates the displacement amount for each of the plurality of markers based on the phase difference of the moiré fringes and the magnitude of the periodic shift; Equipped with Displacement measuring device.

4. The displacement measuring device according to any one of claims 1 to 3, one of the plurality of markers is a reference marker attached to a measurement point treated as a fixed point; the markers other than the reference marker are measurement markers; the marker image analysis unit calculates the displacement amount of each measurement marker as a difference value from the displacement amount of the reference marker; Displacement measuring device.

Images