A laser assisted calibration device and method of using the device

Abstract

The application provides a kind of laser auxiliary calibration device and the use method of the device, and the calibration method steps are as follows: three lasers are irradiated on the measuring surface by adjusting the laser angle, a reference image is collected and saved as a gray image, the calibration object is removed and placed on the multi-dimensional translation stage, the reference image is set as a dark channel, the current gray image is collected in real time and set as a light channel, the dark channel image and the light channel image are synthesized into a real-time image, the calibration plate is placed on the translation stage to collect the image, the corner point information of the calibration plate is extracted, and finally the camera internal and external parameters under ideal conditions are calculated, and the distortion coefficient of radial distortion is obtained by using the least square method;The application can accurately calibrate the detection surface of various parts with different heights and appearances, and can accurately position the detection surface of the measured object, thereby improving the calibration accuracy.

Description

Technical Field

[0001] This invention relates to the field of machine vision image detection, and in particular to a laser-assisted calibration device and a method of using the device. Background Technology

[0002] In image measurement, localization, and machine vision applications, to determine the relationship between the geometric position of a point on the surface of a spatial object in three-dimensional space and its corresponding point in a two-dimensional image, it is necessary to establish a geometric model of the camera imaging. The parameters of this geometric model are the camera parameters, and the process of solving for these parameters is known as camera calibration. Current calibration methods involve placing a calibration plate on the surface to be measured and calculating the parameters by extracting the coordinates of the grid corner points and the camera's intrinsic parameters. However, this process requires ensuring that the calibration plate is placed directly above the surface to be measured, parallel to or coinciding with the measurement surface.

[0003] However, in actual measurements, due to the uncertainty of the surface shape of the calibrated object, problems often arise such as the measurement surface being too small, the measurement surface being blocked by other parts of the object, or the inability to place the calibration plate, leading to the inability to proceed with the testing process normally. For example... Figures 1-4 As shown, the measuring surface is located in the middle region inside the cylinder. Normal calibration requires placing the calibration plate on the internal measuring surface. If a suitable calibration plate cannot be placed on the measuring surface, calibration cannot be performed. Even if placed directly above the cylinder, it cannot be determined whether it is parallel to the measuring surface, thus affecting the validity of the calibration. Furthermore, the calibration plate must be larger than one-third of the camera's field of view during calibration. Both conditions must be met simultaneously for calibration to proceed smoothly. Due to these issues, calibration cannot be performed successfully, thus affecting measurement accuracy. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a laser-assisted calibration device and a method for using the device, which has a simple structure and is easy to use.

[0005] A laser-assisted calibration device for measuring the dimensions of parts of different heights includes a housing, a camera, an adjustment frame, a point light source, an adjustment platform, and a calibration plate. The camera, adjustment frame, and adjustment platform are disposed in the housing. The point light source is disposed in the adjustment frame. The calibration plate is disposed in the adjustment platform. The housing is a hexahedron with one open side, and the other three sides of the housing are provided with adjustment frames. The camera is disposed on the top surface of the housing, and the adjustment platform is disposed on the bottom surface.

[0006] Furthermore, the adjustment bracket is positioned around the camera.

[0007] A laser-assisted calibration method based on the above-mentioned device is characterized by comprising the following steps:

[0008] S1: A point light source marks the surface of the part to be measured;

[0009] S2: The camera records the marked position, the part to be measured is removed, the adjustment platform is placed at the position to be measured, and the point light source marks the surface of the adjustment platform.

[0010] S3: Change the position and orientation of the adjustment stage so that the position of the point light source mark on the surface of the adjustment stage recorded by the camera coincides with the position of the point light source mark in S1;

[0011] S4: Set up a calibration plate for calibration; use the calibration data to measure the dimensions of the original part.

[0012] Furthermore, the steps of marking using a point light source in S1 and S2 include:

[0013] S11: Adjust the adjustment frame so that the point light source emits light onto the detection surface;

[0014] S12: The light emitted by the point light source is reflected by the detection surface and transmitted to the camera;

[0015] S13: Camera captures real-time images.

[0016] Furthermore, step S4 includes the following steps:

[0017] S41: Transformation from world coordinate system to camera coordinate system;

[0018] S42: Transformation from the camera coordinate system to the imaging plane coordinate system, which includes a calibration process.

[0019] S43: Correct the imaging plane coordinate system;

[0020] S44: Transform from the corrected imaging plane coordinate system to the image coordinate system;

[0021] S45: Determine the overall internal and external parameters of the camera and complete the calibration.

[0022] Furthermore, in S41, the transformation from the world coordinate system to the camera coordinate system includes transforming point P... w Convert to point P c Specifically, it is calculated using the following formula:

[0023] P c =R·P w +T

[0024] Where R represents the rotation matrix, T represents the translation vector, and R includes three rotation angles α, β, and γ; the rotation matrix R(α,β,γ) is expressed as:

[0025]

[0026] Where α represents the angle between the camera coordinate system and the X-axis of the world coordinate system, β represents the angle between the camera coordinate system and the Y-axis of the world coordinate system, and γ represents the angle between the camera coordinate system and the Z-axis of the world coordinate system; P c The coordinates in the camera coordinate system are represented as (x... c y c , z c ); T = (t x ,t y ,t z ).

[0027] Furthermore, in step S42, during the transformation from the camera coordinate system to the imaging plane coordinate system, it is necessary to convert P... c The transformation to the imaging plane coordinate system depends on the following transformation relationship:

[0028]

[0029] Where f represents the focal length of the camera; u and v represent the coordinates of point P in the imaging plane coordinate system.

[0030] Furthermore, in S43, the corrected imaging plane coordinate system includes:

[0031]

[0032] Where the parameter k represents the magnitude of the radial distortion; This represents the true imaging plane coordinates of point P after correction.

[0033] Furthermore, in step S44, the coordinates of point P in the ideal imaging plane coordinate system are... Transformation to the image coordinate system includes:

[0034]

[0035] Where C x C y S is the coordinate value of the projection center's perpendicular projection onto the imaging plane coordinate system. x S y It is the distance between adjacent pixels in the horizontal and vertical directions of an image sensor.

[0036] Furthermore, in S45, the process of determining the total internal and external parameters of the camera is as follows: the checkerboard calibration plate is placed above the adjustment platform, and the current image of the calibration plate is captured by the camera. First, the corner coordinates m of the checkerboard are obtained from the image of the calibration plate. i,j The m i,jIn the image coordinate system, the distance d(c) between the projected coordinates Ti(Mi,c) is calculated using the following formula:

[0037]

[0038] By jointly solving two or more images with calibration plates, the minimum value of d(c) is found, and the total camera parameters c = (f, k, S) are determined. x S y C x C y , t x , t y , t z (α, β, γ) to complete the camera calibration process.

[0039] The beneficial effects of this invention are as follows:

[0040] By setting up a point light source and an adjustment platform, the inspection surface of parts with different heights and appearances can be accurately calibrated.

[0041] A planar positioning method is introduced, which can accurately locate the detection surface of the measured object, thereby improving the calibration accuracy;

[0042] By correcting the coordinate system of the imaging plane, the distortion values ​​generated during the imaging process are corrected, making the calibration more accurate. Attached Figure Description

[0043] Figure 1 For the chessboard grid marking board;

[0044] Figure 2 In traditional calibration, the measuring surface is located in the middle region inside the cylinder;

[0045] Figure 3 In traditional calibration, the calibration plate is placed on the testing surface inside the cylinder;

[0046] Figure 4 In traditional calibration, the calibration plate is placed directly above the cylinder;

[0047] Figure 5 This is a simplified schematic diagram of the calibration device of the present invention;

[0048] Figure 6 This is a simplified top view of the calibration device of the present invention;

[0049] Figure 7 This is a structural diagram of the calibration device according to Embodiment 1 of the present invention;

[0050] Figure 8 This is a front view of the calibration device according to Embodiment 1 of the present invention;

[0051] Figure 9 This is a schematic diagram of surface optical path reflection at different tilt angles according to the present invention;

[0052] Figure 10 This is a schematic diagram of the adjustment platform of the present invention;

[0053] Figure 11 This is a bottom view of the base of the present invention;

[0054] Figure 12 This is a perspective view of the base of the present invention;

[0055] Figure 13 This is a perspective view of the adjustment frame of the present invention;

[0056] Figure 14 This is a simplified structural diagram of the object detection surface positioning of the present invention;

[0057] Figure 15 This is a schematic diagram of the detection surface of the object to be measured according to the present invention;

[0058] Figure 16 This is a schematic diagram of camera imaging of the detection surface of the present invention;

[0059] Figure 17 This is a schematic diagram of the adjustment table detection of the present invention;

[0060] Figure 18 This is a schematic diagram of the imaging of the measurement surface restored by the adjustment stage of the present invention;

[0061] Figure 19 This is a schematic diagram of the planar imaging principle of the present invention;

[0062] Figure 20 This is a flowchart of the present invention.

[0063] Attached diagram labels: 1. Box body; 2. Camera; 3. Adjustment frame; 31. Fixing base; 32. Crank arm; 4. Point light source; 5. Adjustment platform; 51. Upright pole; 52. Reflective surface; 53. Knob; 531. Height knob; 532. Positioning knob; 54. Support rod; 541. Connecting rod; 55. Base; 551. Upper base; 552. Lower base; 56. Sliding rod; 57. Sliding block; 58. Fixing block; 59. Height adjustment rod; 6. Calibration plate; 7. Part to be measured. Detailed Implementation

[0064] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0065] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0066] Example 1:

[0067] like Figure 5-8 As shown, a laser-assisted calibration device for measuring the dimensions of parts of different heights includes a housing 1, a camera 2, an adjustment frame 3, a point light source 4, an adjustment platform 5, and a calibration plate 6.

[0068] The housing 1 is a hexahedron with one open side, which is the side of the housing 1. Adjustment frames 3 are provided on the other three sides of the housing 1. A camera 2 is mounted on the top surface of the housing 1, and an adjustment platform 5 is mounted on the bottom surface. The adjustment platform 5 rests only on the bottom surface of the housing and can move on the bottom surface. The point light source 4 is mounted on the adjustment frame 3. The calibration plate 6 is mounted on the adjustment platform 5. The housing 1 can be made of metal; in this embodiment, iron is used. To facilitate operation, a base is provided below the bottom surface of the housing, raising the horizontal height of the adjustment platform. To facilitate the movement of the calibration device, casters are provided at the bottom of the housing, allowing the calibration device to be moved freely.

[0069] like Figure 13 As shown, the adjustment frame 3 is positioned around the camera 2. The adjustment frame 3 is a universal adjustment frame 3, capable of adjusting its horizontal height, tilt angle, and horizontal position. The adjustment frame 3 includes a fixed base 31 and a curved arm 32. The fixed base 31 is equipped with a magnet, allowing the adjustment frame 3 to adhere to the housing 1 and simultaneously adjust its height and angle. The curved arm 32 is hinged to the fixed base 31. A hinge joint is located at the end of the fixed base 31 furthest from the magnet. One end of the hinge joint is threaded and connected to the fixed base 31, while the other end has a spherical hinge block. One end of the curved arm 32 is hinged to the hinge joint of the fixed base 31, and the other end has a similar hinge joint connected to a point light source. The curved arm 32 is composed of two parallel elliptical plates connected by a thread. Circular openings are located at both ends of the elliptical plates, which engage with the spherical hinge blocks.

[0070] like Figure 7 , 13 As shown, there are at least three point light sources 4, with one point light source 4 mounted on each adjustment frame 3, and threads connecting the point light source 4 to the adjustment frame 3. In this embodiment, the point light source 4 is a semiconductor laser, and the number of point light sources 4 is three.

[0071] like Figure 10-12 As shown, the adjustment platform 5 includes a vertical rod 51, a reflective surface 52, a knob 53, a support rod 54, a base 55, and sliding rods 56. The base includes an upper base 551 and a lower base 552. The reflective surface 52 is disposed on the upper surface of the upper base 551, and a vertical rod 51 is disposed between the reflective surface 52 and the upper base 551. There are four vertical rods 51, which are disposed at the four corners of the reflective surface 52. There are four sliding rods 56 in total, arranged in two groups of two. The sliding rods 56 in the same group are parallel and on the same horizontal plane. The two groups of sliding rods 56 are respectively disposed on the lower surface of the upper base 551 and the upper surface of the lower base 552. The knob 53 includes a height knob 531 and a positioning knob 532, which is disposed on the upper base 551 at one end of the sliding rod 56. The positioning knob 532 can lock the height knob 531 to prevent changes in the height of the adjustment platform during calibration. A support rod 54 is also provided between the upper base 551 and the lower base 552. The support rods 54 are arranged crosswise, located on both sides of the slide rod 56, and a connecting rod 541 is provided between the two sides of the support rod to stabilize the support. A slider 57 and a fixed block 58 are provided between the support rod 54 and the slide rod 56, with one slider 57 and one fixed block 58 on each slide rod 56. The slider 57 is sleeved on the slide rod 56 and can slide along the slide rod 56; the fixed block 58 is located at one end of the slide rod 56 and is fixedly connected to the base. The two sides of the slider 57 and the fixed block 58 are hinged to the support rod, and the support rod 54 can rotate around the hinge point. A height adjustment rod 59 is provided on the slider 57 of the slide rod 56 of the upper base 551, and the height adjustment rod 59 is connected to the slider 57 of the upper base 551. The height adjustment lever 59 can extend or retract as the height knob 531 is rotated, pushing the slider 57 located on the upper base 551 to slide along the slide bar 56, thereby adjusting the height of the adjustment platform.

[0072] A laser-assisted calibration method for measuring the dimensions of parts of different heights, the calibration method comprising the following steps:

[0073] S1: The semiconductor laser marks the surface of the part 7 to be tested; the semiconductor laser is mounted on the adjustment frame 3 on both sides of the lens; the adjustment frame 3 is a universal adjustment frame 3, which can adjust the horizontal height, tilt angle and horizontal position of the semiconductor laser.

[0074] S2: Camera 2 records the marked position, removes the part to be tested 7, places the adjustment platform 5 at the position to be tested, and the point light source 4 marks the surface of the adjustment platform 5.

[0075] S3: Change the position and orientation of the adjustment stage 5 so that the position of the point light source 4 on the surface of the adjustment stage 5 recorded by the camera 2 coincides with the position of the point light source 4 in S1.

[0076] S4: Set calibration plate 6 for calibration;

[0077] S5: Use calibration data to measure the dimensions of the original part.

[0078] like Figure 9 , 14 As shown in Figure -20, during the marking processes S1 and S2, the adjustment frame 3 is first adjusted so that the point light source 4 emits light onto the detection surface of the part to be tested 7. In this embodiment, the point light source 4 is a semiconductor laser. Next, the light emitted from the side of the camera 2 by the point light source 4 is reflected by the detection surfaces at different inclinations before reaching the camera 2; this reflection is diffuse reflection. Because the point light source 4 illuminates different positions on the detection surface, its imaging position on the camera 2 will also differ. Therefore, in the image obtained by the camera 2, three points not on the same straight line can determine the position of a plane in space. The position of the plane can be recorded by the imaging position of the bright spots on the image. This invention requires at least three semiconductor lasers for positioning; in this embodiment, three semiconductor lasers are used for positioning.

[0079] In this embodiment, three semiconductor lasers emit lasers that strike the detection surface of the part under test 7. The camera 2 captures images of three dark spots. These images are saved, and then the adjustment platform 5 is placed on top without changing the orientation of the semiconductor lasers. Since the height and tilt angle of the adjustment platform 5 may differ from the detection surface of the part under test 7, the positions of the three laser points may deviate. The camera 2 acquires images of the adjustment platform 5 in real time, and an image processing algorithm synthesizes the images of the detection surface of the part under test 7 and the adjustment platform 5 in real time to observe the position of the bright spots. The height of the four uprights 51 of the adjustment platform 5 is adjusted to control the height and tilt angle of the reflective surface 52 of the adjustment platform 5. When the height and level of the adjustment platform 5 change, the position of the bright spots also changes in real time. Observing the image from the camera 2, when the bright spot moves to coincide with the dark spot, it indicates that the plane containing the detection surface of the part under test 7 coincides with the plane containing the reflective surface 52 of the adjustment platform 5. Then, the calibration plate 6 can be placed above the adjustment platform 5 for calibration.

[0080] like Figure 15 As shown, step S4 includes the following steps:

[0081] S41: First, transform from the world coordinate system to the camera 2 coordinate system;

[0082] S42: Then transform from the camera 2 coordinate system to the imaging plane coordinate system;

[0083] S43: Correct the imaging plane coordinate system;

[0084] S44: Transform from the corrected imaging plane coordinate system to the image coordinate system;

[0085] S45: Determine the total internal and external parameters of camera 2 and complete the calibration.

[0086] In S41, the transformation from the world coordinate system to the camera 2 coordinate system includes the transformation of point P. w Convert to point P c Specifically, it is calculated using the following formula:

[0087] P c =R·P w +T

[0088] Where R represents the rotation matrix, T represents the translation vector, and R includes three rotation angles α, β, and γ. The rotation matrix R(α,β,γ) is expressed as:

[0089]

[0090] Where, T = (t x ,t y ,t z ) is a translation vector; α represents the angle between the camera 2 coordinate system and the world coordinate system's X-axis, β represents the angle between the camera 2 coordinate system and the world coordinate system's Y-axis, and γ represents the angle between the camera 2 coordinate system and the world coordinate system's Z-axis. T and R are the extrinsic parameters of camera 2, used to describe the position of camera 2 in the world coordinate system. The world coordinate system can be transformed to the camera 2 coordinate system through the extrinsic parameters; P c The coordinate values ​​in the camera 2 coordinate system are represented as (x... c y c , z c ).

[0091] In S42, during the transformation from the camera 2 coordinate system to the imaging plane coordinate system, it is necessary to convert P... c The transformation to the imaging plane coordinate system depends on the following transformation relationship:

[0092]

[0093] Where f represents the focal length of camera 2; u and v represent the coordinates of point P in the imaging plane coordinate system.

[0094] Due to lens distortion, the obtained image plane coordinate values ​​u and v differ from the actual image plane coordinate values. To convert the image plane obtained in S42 into the actual image plane, S43 is required: radial distortion correction of the lens.

[0095] The formula for correcting radial distortion of the lens is as follows:

[0096]

[0097] Where the parameter k represents the magnitude of the radial distortion; This represents the true imaging plane coordinates of point P after correction.

[0098] In S44, the coordinates of point P in the ideal imaging plane coordinate system are... Transformation to the image coordinate system includes:

[0099]

[0100] Where C x C y S is the coordinate value of the projection center's perpendicular projection onto the imaging plane coordinate system. x S y It is the distance between adjacent pixels in the horizontal and vertical directions of the image sensor; (f, k, S) x S y C x C y ) represents the intrinsic parameters of camera 2.

[0101] In S45, the process of determining the total internal and external parameters of camera 2 is as follows: Place the checkerboard calibration plate 6 above the adjustment platform 5, and use camera 2 to capture the current image of calibration plate 6. First, perform algorithmic processing on the image of calibration plate 6 obtained by camera 2 to obtain the corner coordinates m of the checkerboard from the image of calibration plate 6. i,j The m i,j In the image coordinate system, the distance d(c) between the projected coordinates Ti(Mi,c) is calculated using the following formula:

[0102]

[0103] By jointly solving two or more images with calibration plate 6, the minimum value of d(c) is found, and the parameters of camera 2 are determined. The total intrinsic and extrinsic parameters of camera 2, c = (f, k, S), are obtained. x S y C x C y , t x , t y , t z (α, β, γ), complete the calibration process of camera 2.

[0104] The above description is merely a specific example of the present invention and does not constitute any limitation on the present invention. Obviously, those skilled in the art, after understanding the content and principles of the present invention, may make various modifications and changes in form and detail without departing from the principles and structure of the present invention; however, these modifications and changes based on the spirit of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. A laser-assisted calibration device, characterized in that, The device includes a housing, a camera, an adjustment frame, a point light source, an adjustment platform, and a calibration plate. The camera, adjustment frame, and adjustment platform are housed within the housing. The point light source is mounted on the adjustment frame. The calibration plate is mounted on the adjustment platform. A base is provided below the bottom of the housing to raise the level of the adjustment platform. Casters are provided at the bottom of the housing to allow for free movement of the calibration device. The point light source is used to mark the surface of the part to be tested; The camera is used to record the position of the point light source marker; The adjustment platform is used to adjust the illumination position of the point light source during the calibration process so that it coincides with the position recorded by the camera; The calibration plate is used for calibration, and the dimensions of the part to be tested are measured using the calibration data. The camera can also correct lens distortion according to a lens radial distortion correction formula, whereby the lens radial distortion correction formula is expressed as: ； Where parameters k Indicates the magnitude of radial distortion; This represents the coordinates of point P in the imaging plane coordinate system; , This represents the true imaging plane coordinates of point P after correction.

2. The laser-assisted calibration device according to claim 1, characterized in that, The adjustment frame is a universal adjustment frame, which can be adjusted in terms of horizontal height, tilt angle, and horizontal position.

3. The laser-assisted calibration device according to claim 1, characterized in that, The adjustment frame includes a fixed base and a curved arm. The fixed base of the adjustment frame is equipped with a magnet, which allows the adjustment frame to be attached to the box and to adjust the height and angle of the adjustment frame. The curved arm is hinged to the fixed base.

4. The laser-assisted calibration device according to claim 3, characterized in that, One end of the curved arm is hinged to the hinge joint of the fixed base, and the other end of the curved arm is provided with a similar hinge joint, which is connected to the point light source.

5. The laser-assisted calibration device according to claim 1, characterized in that, The adjustment bracket is positioned around the camera.

6. A laser-assisted calibration method, characterized in that, This method utilizes a laser-assisted calibration device as described in any one of claims 1-5, and includes the following steps: S1: Point light sources are used to mark the surface of the part to be measured; there are at least three point light sources, one of which is set on an adjustment frame; a thread is provided between the point light source and the adjustment frame; the horizontal height, tilt angle and horizontal position of the point light source can be adjusted by the adjustment frame. S2: The camera records the marked position, the part to be measured is removed, the adjustment platform is placed at the position to be measured, and the point light source marks the surface of the adjustment platform. S3: Change the position and orientation of the adjustment stage so that the position of the point light source mark on the surface of the adjustment stage recorded by the camera coincides with the position of the point light source mark in S1; S4: Set the calibration plate for calibration; The dimensions of the part to be tested are measured using calibration data; The steps for marking using a point light source in S1 and S2 include: S11: Adjust the adjustment frame so that the point light source emits light onto the detection surface; S12: The light emitted by the point light source is reflected by the detection surface and transmitted to the camera; S13: Camera captures real-time images.

7. The laser-assisted calibration method according to claim 6, characterized in that, S4 includes the following steps: S41: Transformation from world coordinate system to camera coordinate system; S42: Transformation from the camera coordinate system to the imaging plane coordinate system, which includes a calibration process. S43: Correct the imaging plane coordinate system; S44: Transform from the corrected imaging plane coordinate system to the image coordinate system; S45: Determine the overall internal and external parameters of the camera and complete the calibration.

8. The laser-assisted calibration method according to claim 7, characterized in that, In the S41, conversion from the world coordinate system to the camera coordinate system is performed, including conversion of the point P w to the point P c , specifically by the following equation: P c = R ·P w +T in R Let T denote the rotation matrix and T denote the translation vector. R include Three rotation angles; rotation matrix R Represented as: ； in, This represents the angle between the camera coordinate system and the world coordinate system's X-axis. This represents the angle between the camera coordinate system and the world coordinate system along the Y-axis. P represents the angle between the camera coordinate system and the world coordinate system along the Z-axis; c The coordinate values ​​in the camera coordinate system are represented as ( ); T= .

9. A laser-assisted calibration method according to claim 8, characterized in that, In step S42, during the transformation from the camera coordinate system to the imaging plane coordinate system, it is necessary to convert P... c The transformation to the imaging plane coordinate system depends on the following transformation relationship: ； in, f Indicates the camera's focal length; This represents the coordinates of point P in the imaging plane coordinate system.

Images