A method for detecting the spacing and center distance of a sunk groove by stitching images of a binocular lens

Abstract

The present invention discloses a method for detecting the spacing and center distance of the sunk grooves by stitching the images of a binocular lens. The steps include: S1, based on a calibration plate and an image processing unit, eliminating the radial distortion and tangential distortion of the binocular optical lens module to obtain a calibrated world coordinate system; S2, the upper camera of the binocular optical lens module takes a picture of the sunk grooves of the shaft part to be measured to obtain the coordinates of the upper sunk grooves in the upper camera coordinate system, and the lower camera of the binocular optical lens module takes a picture of the sunk grooves of the shaft part to be measured to obtain a picture of the lower sunk grooves and establish the coordinates in the lower camera coordinate system. The upper camera coordinate system and the lower camera coordinate system are respectively stitched and mapped into the world coordinate system to obtain the coordinates of the upper sunk grooves and the lower sunk grooves in the world coordinate system; S3, measuring the spacing and center distance of the upper and lower sunk grooves based on the world coordinate system. The present invention can measure the spacing and center distance of the sunk grooves of parts beyond the monocular vision field, and the method is simple and efficient, and has good prospectiveness.

Description

Technical Field

[0001] The present invention belongs to the technical field of shaft part detection, and specifically discloses a method for detecting the spacing and center distance of sunk grooves by binocular lens image stitching. Background Art

[0002] Shaft parts are widely used in various industrial sectors, especially in automobile assembly production. In the manufacturing of some shaft parts, the final products leaving the factory need to be measured for dimensions and evaluated for product quality in strict accordance with standards, and the results are recorded and analyzed to guide subsequent production. Traditional measurements are carried out by manual sampling and using handheld instruments, and data recording is mainly done by manual transcription. So far, existing optical measurement solutions are all equipped with a single monocular lens and a light source, and can only measure small-sized circles. Their application limitations are narrow measurement ranges, inability to measure the spacing and center distance of sunk grooves of large-sized shaft parts, and measurement accuracy depending on the experience of the measurer, with poor measurement identity and inability to accumulate a large amount of measurement data for big data analysis. At the same time, relying on manual quality inspection is cumbersome and labor-intensive, requires high requirements for quality inspectors, and the personal subjectivity of quality inspectors will have a certain impact on measurement and quality evaluation. Quality inspection data cannot be stored in a formatted manner, which is also not conducive to subsequent product quality traceability and improving the production line with quality inspection data to increase the product qualification rate. Summary of the Invention

[0003] Aiming at the technical problems existing in the prior art, the present invention provides a method for detecting the spacing and center distance of sunk grooves by binocular lens image stitching. It uses binocular lenses, a light source and a calibration piece, stitches the images of the upper and lower sunk grooves into one image through stitching technology, and measures the dimensions of the sunk grooves on this stitched single image. It can measure the spacing and center distance of the sunk grooves of parts beyond the monocular vision field, and the method is simple and efficient, and has good prospectiveness. Future products may develop in this direction.

[0004] The present invention discloses a method for detecting the spacing and center distance of sunk grooves by binocular lens image stitching, which is used to measure the spacing and center distance of the sunk grooves of a to-be-detected shaft part, and includes two sets of binocular optical lens modules arranged up and down. Each set of binocular optical lens modules includes a camera and a light source that are symmetrically arranged on both sides of the to-be-detected shaft part and coaxially arranged:

[0005] S1, based on a calibration board and an image processing unit, eliminate the radial distortion and tangential distortion of the binocular optical lens module, and obtain a calibrated world coordinate system;

[0006] In S2, the upper camera of the binocular optical lens module captures the sinking groove of the shaft-like part to be measured to obtain the coordinates of the upper sinking groove in the coordinate system of the upper camera. The lower camera of the binocular optical lens module captures the sinking groove of the shaft-like part to be measured to obtain a photo of the lower sinking groove and establish the coordinates of the lower camera coordinate system. The upper camera coordinate system and the lower camera coordinate system are respectively spliced and mapped into the world coordinate system to obtain the coordinates of the upper sinking groove and the lower sinking groove in the world coordinate system;

[0007] In S3, based on the world coordinate system, the distance and the center distance between the upper and lower sinking grooves are measured.

[0008] In a preferred implementation of the present invention, in S1, the specific steps include:

[0009] In S11, fix the lens and the light source, and adjust the center lines of the single set of lens and the light source to be on the same straight line;

[0010] In S12, adjust the center lines of the two sets of optical lens systems to be collimated. The distance between the two sets of lenses is adjusted according to the length of the calibration plate, so that the midpoints of the boundaries on both sides of the object to be measured fall on the center line of the optical system as much as possible;

[0011] In S13, adjust the calibration plate or the binocular vision system so that the pictures taken by the two sets of cameras are both the clearest;

[0012] In S14, start the image processing unit, take the projection photos of the upper end and the lower end of the calibration piece, eliminate the radial distortion of the two lenses, then eliminate the tangential distortion, and calculate the coefficients of the equations for eliminating the radial distortion and the tangential distortion.

[0013] In a preferred implementation of the present invention, in S14, the steps for eliminating distortion include:

[0014] k 1 , k 2 are radial distortion parameters, p 1 , p 2 are tangential distortion parameters, r 2 is the known radius of the distortion circle, (x, y) is the coordinate point of the image before distortion, (x ^ , y ^ ) is the coordinate point after correction. Since (x ^ , y ^ ) is the checkerboard or dot matrix calibration diagram, whose coordinates are known, (x, y) is the coordinate of the actual photo. By (x ^ , y ^ ) and (x, y), calculate the k 1 , k 2 and p 1 , p 2 parameters. For mirror distortion, substitute the taken photo into Formulas 1 and 2 for calculation:

[0015] x ^ = x + x[k 1 (x 2 + y 2 ) 2 + k 2 (x 2 + y 2 ) 2 ) (1)

[0016] y ^ = y + y[k 1 (x 2 + y 2 ) 2 + k 2 (x 2 + y 2 ) 2 ) (2)

[0017] For tangential distortion, as shown in Formulas 3 and 4:

[0018] x ^ = x + [2p 1 xy + p 2 (r 2 + 2x 2 )] (3)

[0019] y ^ = y + [2p 1 (r 2 + 2y 2 ) + 2p 2 xy] (4).

[0020] In a preferred embodiment of the present invention, in S14, for the image with distortion removed and the width W a and length L a of the calibration plate are calculated. By edge finding, line segment measurement, and two-dimensional coordinate transformation, etc., the rotation angles θ1, θ2 of each camera relative to the calibration plate, the unit pixels μ1, μ2, and the midpoints P1, P2 of the upper and lower image calibration plates are obtained. The P 1 (x p1 , y p1 ) and P 2 (x p2 , y p2 ) coordinates are based on the known dimensions of the calibration plate. According to W a it can be obtained that the mapped points of P1 and P2 in the world coordinate system are:

[0021] x wp1 = x wp2 = 0 (5)

[0022]

[0023]

[0024] Among them, the calibrated plate pixel width value measured by the upper camera is denoted as W U , and the pixel width value measured by the lower camera is denoted as W L , then the calculation methods of μ1 and μ2 are as follows:

[0025]

[0026]

[0027] Through the above steps, the axis directions and origin of the world coordinate system, as well as the mapping points of each point in the upper and lower cameras in the world coordinate system, can be obtained.

[0028] In a preferred implementation manner of the present invention, in S2,

[0029] For the upper camera, its internal point is (x u , y u ), and the corresponding point in the world coordinate system is (x world , y world ):

[0030] x world = cosθ 1 μ 1 (x u - x p1 ) (8)

[0031] y world = sinθ 1 μ 1 (y u - y wp1 ) (9)

[0032] For the lower camera, its internal point is (x l , y l ), and the corresponding point in the world coordinate system is (x world , y world ):

[0033] x world = cosθ 1 μ 2 (x u - x p2 ) (10)

[0034] y world = cosθ 1 μ 2 (y u + y wp2 ) (11)

[0035] After the calibration plate image is recalculated and output by the radial distortion and tangential distortion equations with determined coefficients, a world coordinate system obtained based on the calibration plate and the center line of the binocular vision system is calculated on this basis.

[0036] In a preferred embodiment of the present invention, in S3, the specific steps include,

[0037] S31, Based on the calibrated camera lens and the frame, place the shaft part between the two groups of lenses so that one group of lenses can clearly capture the projection of the sunk groove of the shaft part, and the other group of lenses clearly captures the projection of the sunk groove on the other side;

[0038] S32, Use the camera to take 2 photos of the sunk grooves of the shaft part and input them into the vision processing unit for image calculation;

[0039] S33, The vision processing system first maps and splices the two pictures according to the calibrated world coordinate system, synthesizes and outputs them into one image;

[0040] S34, On this spliced image, fit the center of the sunk groove by the least squares method, find the centers of the upper sunk groove and the lower sunk groove and record them as C u (x u ,y u ), C l (x l ,y l ), and according to the formula

[0041] x world =cosθ 1 μ 1 (x u -x p1 ) (8)

[0042] y world =sinθ 1 μ 1 (y u -y wp1 ) (9)

[0043] x world =cosθ 1 μ 2 (x u -x p2 ) (10)

[0044] y world =cosθ 1 μ 2 (y u +y wp2 ) (11)

[0045] Convert to point C in the world coordinate system 1 (x 1 ,y 1 ), C 2 (x 2 ,y 2 ), then the center distance D of the sinking groove 1 is:

[0046]

[0047] Because the line connecting the two centers may not be perpendicular to the axis of the vertical axis, its x 1 and x 2 may not be equal, so there may be an offset between the centers of the upper and lower sinking grooves;

[0048] S35. Perform contour fitting on the upper and lower camera straight lines, determine the straight line equations of the upper and lower outer diameters, take 2 points on the contour fitting points, and convert them into point positions in the world coordinate system through formulas (8)(9), (10)(11), where:

[0049] The upper camera point is denoted as: a u1 (x 1 ,y 1 ) a u2 (x 2 ,y 2 )

[0050] The lower camera point is denoted as: a l1 (x 3 ,y 4 ) a l2 (x 3 ,y 4 )

[0051] Its straight line equation is:

[0052]

[0053] Since the two straight lines are not necessarily parallel, the upper camera point a u1 (x 1 ,y 1 ) is used to solve the distance to the lower camera straight line, and the shaft diameter can be obtained, denoted as D 2 :

[0054] Assume that the fitted straight line of the lower camera is:

[0055] ax + by + c = 0 (14)

[0056] where

[0057]

[0058] Then

[0059]

[0060] In a preferred embodiment of the present invention, the device includes a manipulator, a measurement system, a binocular optical lens module, and a manipulator control system. The manipulator control system is electrically connected to the manipulator, and the binocular optical lens module is connected to the mobile end of the manipulator; the binocular optical lens module includes a frame for connecting the manipulator, and on the frame, there are V-shaped positioning blocks and U-shaped cantilevers arranged at intervals along the axial direction of the shaft-like part to be measured. On the U-shaped cantilever, there are two groups of photographing units arranged at intervals up and down for photographing the sunk grooves on the shaft-like part to be measured. Each photographing unit includes a camera and an illumination light source arranged coaxially, and the camera and the illumination light source are symmetrically arranged on both sides of the shaft-like part to be measured. The camera is electrically connected to the measurement system.

[0061] In a preferred embodiment of the present invention, the symmetry axis of the V-shaped positioning block coincides with the symmetry axis of the U-shaped cantilever.

[0062] In a preferred embodiment of the present invention, the V-shaped positioning block includes two positioning inclined planes symmetrically arranged with respect to the central axis of the shaft-like part to be measured.

[0063] In a preferred embodiment of the present invention, a quick-change joint for connecting the manipulator is provided on the frame.

[0064] The present invention also discloses a method for detecting the spacing and center distance of sunk grooves by binocular lens image stitching, which includes a support frame for positioning and carrying the shaft-like part to be measured. A three-axis motion unit is arranged beside the support frame, and an image acquisition and processing unit is connected to the mobile end of the three-axis motion unit; the three-axis motion unit includes a fixed gantry. A processing unit is provided on the fixed gantry. On the fixed gantry, there is a first linear module arranged along the axial direction of the shaft-like part to be measured. The mobile end of the first linear module is connected to a second linear module arranged perpendicular to it. The mobile end of the second linear module is provided with a third linear module arranged in the vertical direction. On the mobile end of the third linear module, there are symmetrically arranged connecting cantilevers. On the connecting cantilevers, there are two groups of image acquisition and processing units arranged at intervals up and down. Each image acquisition and processing unit includes a photographing camera, a light source, and a data processing unit. The photographing camera and the light source are arranged coaxially, the photographing camera is electrically connected to the data processing unit, and the photographing camera and the light source are symmetrically arranged on both sides of the shaft-like part to be measured.

[0065] In a preferred embodiment of the present invention, a stepping transmission unit for driving the support frame to move along the axial direction of the shaft-like part to be measured is connected to the support frame.

[0066] In a preferred embodiment of the present invention, an infrared trigger unit for triggering the camera to take pictures is provided beside the support gantry.

[0067] In a preferred embodiment of the present invention, the connecting cantilever is of H shape.

[0068] In a preferred embodiment of the present invention, the fixed gantry includes bases symmetrically arranged on both sides of the support gantry and a gantry connected to the two bases.

[0069] The present invention also discloses a method for optically detecting a counterbore groove, which includes a method for detecting the spacing and center distance of the counterbore groove by binocular lens image stitching.

[0070] The beneficial effects of the present invention are as follows: The structure of the present invention is simple and convenient to use. It uses a binocular vision system (camera, light source, lens, vision controller) in cooperation with a calibration piece to take pictures of the calibration piece, and uses a calibration algorithm to eliminate lens distortion. At the same time, the world coordinate system of the binocular vision system is calibrated. Then, the upper and lower counterbore grooves of the shaft part are photographed by the binocular lens, and the upper and lower counterbore groove images are stitched and mapped into the world coordinate system. The spacing and center distance of the upper and lower counterbore grooves are measured through the world coordinate system, solving the problem of difficult measurement of the spacing and center distance of the counterbore grooves of large-diameter shaft parts by monocular vision. It belongs to a new measurement method for measuring the counterbore groove and center distance based on the binocular vision system; further, the present invention realizes the automatic measurement of the counterbore groove of the shaft through the use of a binocular optical system module, which has high measurement flexibility and high measurement accuracy. It can be deployed online and is suitable for non-contact and efficient measurement of the counterbore grooves of various types of shaft parts. The measurement data can be quantitatively analyzed, with good prospectiveness, and future products may develop in this direction; further, the V-shaped positioning block of the present invention can eliminate the mechanical positioning error of the manipulator, so as to measure parameters such as the radius of the counterbore groove, the center distance of the counterbore groove, and the bottom spacing of the counterbore groove of the shaft part fully automatically, with high precision and high flexibility. Description of the Drawings

[0071] Figure 1 is a flowchart of a method for detecting the spacing and center distance of a counterbore groove by binocular lens image stitching according to the present invention;

[0072] Figure 2 is a schematic diagram of the shooting state of a method for detecting the spacing and center distance of a counterbore groove by binocular lens image stitching according to the present invention;

[0073] Figure 3 is a schematic diagram of the coordinate system of a method for detecting the spacing and center distance of a counterbore groove by binocular lens image stitching according to the present invention;

[0074] Figure 4 is a schematic diagram of the camera of a method for detecting the spacing and center distance of a counterbore groove by binocular lens image stitching according to the present invention;

[0075] Figure 5 It is a measurement schematic diagram of a method for detecting the spacing and center distance of a counterbore groove by binocular lens image stitching in the present invention;

[0076] Figure 6 It is a schematic diagram of a method for detecting the spacing and center distance of a counterbore groove by binocular lens image stitching in the present invention;

[0077] Figure 7 It is a front view of a method for detecting the spacing and center distance of a counterbore groove by binocular lens image stitching in the present invention;

[0078] Figure 8 It is a side view of a method for detecting the spacing and center distance of a counterbore groove by binocular lens image stitching in the present invention

[0079] Figure 9 It is a schematic diagram of a method for detecting the spacing and center distance of a counterbore groove by binocular lens image stitching in the present invention;

[0080] In the figure: 1 - manipulator; 2 - measurement system; 3 - binocular optical lens module; 4 - manipulator control system; 5 - shaft-like part to be measured; 6 - support bench; 7 - stepping transmission unit; 8 - three-axis motion unit; 9 - infrared trigger unit; 10 - image acquisition and processing unit; 31 - frame; 32 - V-shaped positioning block; 33 - U-shaped cantilever; 34 - camera; 35 - illumination light source; 51 - counterbore groove; 81 - fixed gantry; 82 - first linear module; 83 - second linear module; 84 - third linear module; 85 - connecting cantilever; 101 - shooting camera; 102 - light source. Specific implementation manners

[0081] The technical solutions (including the preferred technical solutions) of the present invention will be further described in detail below by way of the accompanying drawings and by listing some optional embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without making creative efforts shall fall within the scope of protection of the present invention.

[0082] In the description of the present application, it should be noted that the orientation or positional relationship indicated by terms such as "upper" and "lower" is based on the orientation or positional relationship shown in the drawings. This is only for the convenience of describing the present application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation to the present application. Unless otherwise clearly specified and defined, the terms "installed", "connected", and "coupled" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present application can be understood according to specific circumstances.

[0083] Furthermore, in the present application, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprising", "including" or any other variation thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising one..." does not exclude the existence of additional identical elements in the process, method, article or device comprising the said element.

[0084] The present invention discloses a method for detecting the spacing and center distance of the sinking grooves by binocular lens image stitching. A method for detecting the spacing and center distance of the sinking grooves by binocular lens image stitching is used to measure the spacing and center distance of the sinking grooves of the shaft-like part 5 to be measured, and includes two groups of binocular optical lens modules 3 arranged up and down. Each group of binocular optical lens modules 3 includes a camera and a light source symmetrically arranged on both sides of the shaft-like part 5 to be measured and coaxially arranged:

[0085] S1, based on the calibration plate and the image processing unit, eliminate the radial distortion and tangential distortion of the binocular optical lens module 3 to obtain the calibrated world coordinate system;

[0086] S2, the upper camera of the binocular optical lens module 3 takes a picture of the sinking groove of the shaft-like part 5 to be measured to obtain the coordinates of the upper sinking groove in the upper camera coordinate system. The lower camera of the binocular optical lens module 3 takes a picture of the sinking groove of the shaft-like part 5 to be measured to obtain a picture of the lower sinking groove and establish the coordinates of the lower camera coordinate system. Map the upper camera coordinate system and the lower camera coordinate system to the world coordinate system respectively, and obtain the coordinates of the upper sinking groove and the lower sinking groove in the world coordinate system;

[0087] S3. Measure the spacing and center distance of the upper and lower sinking grooves based on the world coordinate system.

[0088] In a preferred embodiment of the invention, in S1, the specific steps include:

[0089] S11. Fix the lens and light source, and adjust the center lines of the single set of lens and light source so that they are on the same straight line;

[0090] S12. Adjust the center lines of the two sets of optical lens systems to be collimated. The distance between the two sets of lenses is adjusted according to the length of the calibration plate, so that the midpoints of the boundaries on both sides of the object to be measured fall on the center line of the optical system as much as possible;

[0091] S13. Adjust the calibration plate or the binocular vision system so that the pictures taken by the two sets of cameras are both the clearest;

[0092] S14. Start the image processing unit, take the projection photos of the upper and lower ends of the calibration piece, eliminate the radial distortion of the two lenses, then eliminate the tangential distortion, and calculate the coefficients of the equations for eliminating the radial distortion and tangential distortion.

[0093] In a preferred embodiment of the invention, in S14, the steps for eliminating distortion include:

[0094] k 1 , k 2 is the radial distortion parameter, p 1 , p 2 is the tangential distortion parameter, r 2 is the known radius of the distortion circle, (x, y) is the coordinate point of the image before distortion, (x ^ , y ^ ) is the corrected coordinate point. Since (x ^ , y ^ ) is the checkerboard or dot matrix calibration pattern, whose coordinates are known, (x, y) is the coordinate of the actual photo. By using (x ^ , y ^ ) and (x, y) to calculate the k 1 , k 2 and p 1 , p 2 parameters. For mirror distortion, substitute the taken photo into Formulas 1 and 2 for calculation:

[0095] x ^ = x + x[k 1 (x 2 + y 2 ) 2 + k 2 (x 2 + y 2 ) 2 (1)

[0096] y ^ = y + y[k 1 (x 2 + y 2 ) 2 + k 2 (x 2 + y 2 ) 2 ) (2)

[0097] For tangential distortion, as shown in Formulas 3 and 4:

[0098] x ^ = x + [2p 1 xy + p 2 (r 2 + 2x 2 )] (3)

[0099] y ^ = y + [2p 1 (r 2 + 2y 2 ) + 2p 2 xy] (4).

[0100] In a preferred embodiment of the invention, in S14, for the image with distortion removed together with the width W a and length L a of the calibration board are calculated. By edge searching, line segment measurement, and two-dimensional coordinate transformation, etc., the rotation angles θ1 and θ2 of each camera relative to the calibration board, the unit pixels μ1 and μ2, and the midpoints P1 and P2 of the upper and lower image calibration boards are obtained. The P 1 (x p1 , y p1 ) and P 2 (x p2 , y p2 ) coordinates are based on the known dimensions of the calibration board. According to W a the mapped points of P1 and P2 in the world coordinate system can be obtained as:

[0101] x wp1 = x wp2 = 0 (5)

[0102]

[0103]

[0104] Among them, the pixel width value of the calibration board measured by the upper camera is denoted as W U , and the pixel width value measured by the lower camera is denoted as W L . Then the calculation methods of μ1 and μ2 are as follows:

[0105]

[0106]

[0107] Through the above steps, the axis directions and origin of the world coordinate system, as well as the mapped points of each point in the upper and lower cameras in the world coordinate system, can be obtained.

[0108] In a preferred embodiment of the invention, in S2,

[0109] For the upper camera, its internal point is (x u , y u ), and the corresponding point in the world coordinate system is (x world , y world ):

[0110] x world = cosθ 1 μ 1 (x u - x p1 ) (8)

[0111] y world = sinθ 1 μ 1 (y u - y wp1 ) (9)

[0112] For the lower camera, its internal point is (x l , y l ), and the corresponding point in the world coordinate system is (x world , y world ):

[0113] x world = cosθ 1 μ 2 (x u - x p2 ) (10)

[0114] y world = cosθ 1 μ 2 (y u + y wp2 ) (11)

[0115] After the calibration plate image is recalculated and output through the radial distortion and tangential distortion equations of the determined coefficients, on this basis, the world coordinate system obtained based on the calibration plate and the center line of the binocular vision system is calculated.

[0116] In a preferred embodiment of the invention, the specific steps in S3 include

[0117] S31. Based on the calibrated camera lens and the frame, place the shaft-like part between the two groups of lenses so that one group of lenses can clearly capture the projection of the sunk groove of the shaft-like part, and the other group of lenses can clearly capture the projection of the sunk groove on the other side.

[0118] S32. Use the camera to take 2 photos of the sunk grooves of the shaft-like part and input them into the vision processing unit for image calculation.

[0119] S33. According to the calibrated world coordinate system, the vision processing system first maps and splices the two pictures through the world coordinate system, synthesizes them and outputs them as one image.

[0120] S34. On this spliced image, fit the center of the sunk groove by the least square method, find the centers of the upper sunk groove and the lower sunk groove and denote them as C u (x u ,y u ), C l (x l ,y l ), and according to the formula

[0121] x world =cosθ 1 μ 1 (x u -x p1 ) (8)

[0122] y world =sinθ 1 μ 1 (y u -y wp1 ) (9)

[0123] x world =cosθ 1 μ 2 (x u -x p2 ) (10)

[0124] y world =cosθ 1 μ 2 (y u +y wp2 ) (11)

[0125] Convert it into the points C 1 (x 1 ,y 1 )、C 2 (x 2 ,y 2 ) in the world coordinate system, then the center distance D 1 of the sunk groove is:

[0126]

[0127] Since the line connecting the two centers may not be perpendicular to the axis of the vertical axis, its x 1 and x 2 may not be equal, so there may be an offset between the centers of the upper and lower sinking grooves;

[0128] S35. Perform contour fitting on the upper and lower camera lines, determine the equations of the upper and lower outer diameter lines, take 2 points on the points of the contour fitting, and convert them into the point positions in the world coordinate system through formulas (8)(9), (10)(11), where:

[0129] The upper camera point is denoted as: a u1 (x 1 , y 1 )a u2 (x 2 , y 2 )

[0130] The lower camera point is denoted as: a l1 (x 3 , y 4 )a l2 (x 3 , y 4 )

[0131] Its line equation is:

[0132]

[0133] Since the two lines are not necessarily parallel, the upper camera point a u1 (x 1 , y 1 ) is used to solve the distance to the lower camera line, and then the shaft diameter can be obtained, denoted as D 2 :

[0134] Let the fitting line of the lower camera be:

[0135] ax + by + c = 0 (14)

[0136] where

[0137]

[0138] Then

[0139]

[0140] In a preferred embodiment of the invention, the device for the method of the present invention includes a manipulator 1, a measurement system 2, a binocular optical lens module 3, and a manipulator control system 4. The manipulator control system 4 is electrically connected to the manipulator 1, and the binocular optical lens module 3 is connected to the mobile end of the manipulator 1. The binocular optical lens module 3 includes a frame 31 for connecting the manipulator 1. On the frame 31, there are V-shaped positioning blocks 32 and U-shaped cantilevers 33 arranged at intervals along the axial direction of the shaft-like part 5 to be measured. On the U-shaped cantilever 33, there are two groups of photographing units arranged at intervals up and down for photographing the undercut grooves on the shaft-like part 5 to be measured. Each photographing unit includes a camera 34 and a lighting source 35 arranged coaxially. The camera 34 and the lighting source 35 are symmetrically arranged on both sides of the shaft-like part 5 to be measured, and the camera 34 is electrically connected to the measurement system 2.

[0141] In a preferred embodiment of the present invention, the symmetry axis of the V-shaped positioning block 32 coincides with the symmetry axis of the U-shaped cantilever 33.

[0142] In a preferred embodiment of the present invention, the V-shaped positioning block 32 includes two positioning inclined planes symmetrically arranged with respect to the central axis of the shaft-like part 5 to be measured.

[0143] In a preferred embodiment of the present invention, a quick-change joint for connecting the manipulator 1 is provided on the frame 31.

[0144] In a preferred embodiment of the present invention, the binocular optical lens module 3 can move along the axis of the shaft-like part 5, adjust the focal length, and rotate 180 degrees around the quick-change joint under the control of the manipulator 1.

[0145] The working steps of the present invention include:

[0146] Step 1: Fix the binocular optical system and the motion control manipulator through a quick-change joint;

[0147] Step 2: Fix the shaft-like part, or deploy the manipulator to the production line so that the shaft-like part is within the movement range of the manipulator;

[0148] Step 3: First, calibrate the binocular optical system using a calibration plate, adjust the lens focal length and the distance of the light source to make the imaging clear, eliminate lens distortion, and determine the world coordinate system;

[0149] Step 4: Teach the motion control system or input the undercut groove coordinates according to the drawing, so that the manipulator can drive the binocular optical system to automatically move above each position of the shaft-like part where the undercut groove size needs to be measured in turn, and make the lens axis and the center of the undercut groove in the same vertical plane;

[0150] Step 5: According to whether the sinking groove is on the left or right side, the manipulator determines whether it is necessary to rotate the optical module together with the V-block 180 degrees along the Z-axis according to the program, so that the V-shaped positioning block will not interfere with the sinking groove;

[0151] Step 6: The manipulator descends to make the V-shaped positioning block stuck on the crankshaft. Through the V-shaped positioning block, it is ensured that the optical axis center line of the optical system is perpendicular to the axis, and the images of the sinking grooves taken by the binocular lens are clear and sharp;

[0152] Step 7: When running to each sinking groove position, the measurement software takes pictures of the upper and lower sinking grooves. After eliminating distortion algorithm, image stitching and synthesis, then through operators such as circle fitting, line finding, and angle calculation, measurement values such as the center distance, bottom distance, and radius of the sinking groove are calculated;

[0153] Step 6: Each measurement data is saved to the database for the user to analyze;

[0154] Step 7: The motion control system records the coordinate schemes of different products and saves them as product recipe programs. Different products only need to call different recipe programs with one key to execute, and rapid and efficient product changeover can be achieved.

[0155] The present invention also discloses a method for detecting the spacing and center distance of sinking grooves by binocular lens image stitching, which includes a support frame 6 for positioning and carrying the shaft-like part 5 to be measured. There is a three-axis motion unit 8 beside the support frame 6, and the mobile end of the three-axis motion unit 8 is connected with an image acquisition and processing unit 10; the three-axis motion unit 8 includes a fixed gantry 81, a processing unit is arranged on the fixed gantry 81, a first linear module 82 arranged along the axial direction of the shaft-like part 5 to be measured is arranged on the fixed gantry 81, the mobile end of the first linear module 82 is connected with a second linear module 83 arranged perpendicular to it, the mobile end of the second linear module 83 is provided with a third linear module 84 arranged in the vertical direction, symmetric connecting cantilevers 85 are arranged on the mobile end of the third linear module 84, and two groups of image acquisition and processing units 10 arranged at intervals up and down are arranged on the connecting cantilevers 85. Each image acquisition and processing unit 10 includes a shooting camera 101, a light source 102 and a data processing unit. The shooting camera 101 and the light source 102 are coaxially arranged, the shooting camera 101 is electrically connected with the data processing unit, and the two image acquisition and processing units 10 can share a data processing unit. The shooting camera 101 and the light source 102 are symmetrically arranged on both sides of the shaft-like part 5 to be measured.

[0156] In a preferred implementation scheme of the present invention, the first linear module 82, the second linear module 83, and the third linear module 84 can be selected as slide modules, and any two of the first linear module 82, the second linear module 83, and the third linear module 84 are arranged perpendicular to each other.

[0157] In a preferred embodiment of the present invention, the image acquisition and processing unit 10 can be used to acquire and process part pictures and obtain processing results, and the obtained results include the shaft diameter sizes of each section of the shaft-type part and the contour modeling dot matrix information.

[0158] In a preferred embodiment of the present invention, a stepping transmission unit 7 for driving the support bench 6 to move axially along the shaft-type part 5 to be measured is connected to the support bench 6. The stepping transmission unit 7 may include a stepping motor, a stepping motor controller, and a transmission structure; the stepping transmission unit 7 communicates with the industrial computer through a PLC, and the industrial computer sends a speed regulation signal to the motor controller to control the transmission of the part to be measured on the support bench 6.

[0159] In a preferred embodiment of the present invention, an infrared trigger unit 9 for triggering the camera to take pictures is arranged beside the support bench 6. The infrared trigger unit 9 includes an infrared emission and reception device. The infrared emission port is collimated and directly opposite to the reception port, and the connection line between the emission device and the reception device is perpendicular to the longitudinal axis of the support bench 6. When the shaft-type part 5 to be measured is transmitted to a preset area, it blocks the infrared light, and the infrared trigger unit 9 generates a pulse signal and transmits it to the industrial computer through the IO interface board, and the industrial computer triggers the shooting camera 84 to acquire pictures.

[0160] In a preferred embodiment of the present invention, the shooting camera 84 can be selected as a ten-million-pixel area array industrial camera; an industrial lens with better anti-distortion performance is equipped at the end of the shooting camera 84, and the light source 85 is a highly collimated industrial light source. The part to be measured triggers the infrared trigger unit 9 to generate a photo-taking pulse signal and sends it to the industrial computer, and the industrial computer triggers the shooting camera 84 to take pictures of the part and processes to obtain the result.

[0161] In a preferred embodiment of the present invention, the connecting cantilever 85 is of H type.

[0162] In a preferred embodiment of the present invention, the fixed gantry 81 includes bases symmetrically arranged on both sides of the support bench 6 and a gantry connected to the two bases.

[0163] The present invention also discloses a sunk groove optical detection system, which includes a method for detecting the spacing and center distance of the sunk groove by binocular lens image stitching.

[0164] The following further explains the operation method of the present invention with reference to the drawings:

[0165] Advanced calibration, and its calibration steps:

[0166] Step 1: Fix the lens and the light source, and adjust the center lines of the single set of lens and the light source so that they are on the same straight line.

[0167] Step 2: Align the centerlines of the two sets of optical lens systems to be collinear. Adjust the distance between the two lenses according to the length of the calibration plate so that the midpoints of the boundaries on both sides of the object to be measured fall as close as possible on the centerline of the optical system.

[0168] Step 3: Adjust the calibration plate or the binocular vision system so that the images captured by the two cameras are both the clearest.

[0169] Step 4: Start the image processing unit, take the projection photos of the upper and lower ends of the calibration piece, eliminate the radial distortion of the two lenses, then eliminate the tangential distortion, and calculate the coefficients of the equations for eliminating the radial distortion and tangential distortion.

[0170] The steps to eliminate distortion are as follows:

[0171] k 1 , k 2 are the radial distortion parameters, p 1 , p 2 are the tangential distortion parameters, r 2 is the known radius of the distortion circle, (x, y) is the coordinate point of the image before distortion, (x ^ , y ^ ) is the coordinate point after correction. Since (x ^ , y ^ ) is the checkerboard or dot matrix calibration chart with known coordinates, and (x, y) is the coordinate of the actual captured image. Therefore, through (x ^ , y ^ ) and (x, y), the k 1 , k 2 and p 1 , p 2 parameters of each pixel can be calculated.

[0172] For mirror distortion, substitute the captured image into Formulas 1 and 2 for calculation:

[0173] x ^ = x + x[k 1 (x 2 + y 2 ) 2 + k 2 (x 2 + y 2 ) 2 (1)

[0174] y ^ = y + y[k 1 (x 2 + y 2 ) 2 + k 2 (x 2 + y 2 ) 2 (2)

[0175] For tangential distortion, as shown in Formulas 3 and 4:

[0176] x ^ = x + [2p 1 xy + p 2 (r 2 + 2x 2 )] (3)

[0177] y ^ = y + [2p 1 (r 2 + 2y 2 ) + 2p 2 xy] (4)

[0178] Step Five: Calculate the undistorted image together with the width W a and length L a of the calibration board. By edge detection, line segment measurement, and two-dimensional coordinate transformation, etc., obtain the rotation angles θ1 and θ2 of each camera relative to the calibration board, the unit pixels μ1 and μ2, and the midpoints P1 and P2 of the upper and lower image calibration boards. The P 1 (x p1 , y p1 ) and P 2 (x p2 , y p2 ) coordinates are based on the known dimensions of the calibration board. According to W a , the mapped points of P1 and P2 in the world coordinate system are:

[0179] x wp1 = x wp2 = 0 (5)

[0180]

[0181]

[0182] Among them, the pixel width value of the calibration board measured by the upper camera is denoted as W U , and the pixel width value measured by the lower camera is denoted as W L . Then, the calculation methods of μ1 and μ2 are as follows:

[0183]

[0184]

[0185] Through the above steps, the axis directions and origin of the world coordinate system, as well as the mapped points of each point in the upper and lower cameras in the world coordinate system, can be obtained.

[0186] For the upper camera, its internal point is (x u , yu ), and the corresponding point in the world coordinate system is (x world , y world ):

[0187] x world = cosθ 1 μ 1 (x u - x p1 ) (8)

[0188] y world = sinθ 1 μ 1 (y u - y wp1 ) (9)

[0189] For the lower camera, its internal point is (x l , y l ), and the corresponding point in the world coordinate system is (x world , y world ):

[0190] x world = cosθ 1 μ 2 (x u - x p2 ) (10)

[0191] y world = cosθ 1 μ 2 (y u + y wp2 ) (11)

[0192] Step 6: After recalculating and outputting the calibration plate image through the radial distortion and tangential distortion equations with determined coefficients, calculate the world coordinate system obtained based on the calibration plate and the center line of the binocular vision system on this basis.

[0193] Perform measurements based on the calibrated parameters, and the measurement steps are as follows:

[0194] Step 1: Based on the calibrated camera lens and the frame, place the shaft parts between the two groups of lenses so that one group of lenses can clearly capture the projection of the sinking groove of the shaft parts, and the other group of lenses can clearly capture the projection of the sinking groove on the other side.

[0195] Step 2: Use the camera to take 2 photos of the sinking grooves of the shaft parts and input them into the vision processing unit for image calculation.

[0196] Step 3: According to the calibrated world coordinate system, the vision processing system first maps and stitches the two pictures through the world coordinate system, synthesizes them, and outputs them as one image.

[0197] Step 4. On this spliced image, as Figure 3 , use the least squares method to fit the center of the sinking groove, and find the centers of the upper and lower sinking grooves, denoted as C u (x u ,y u ), C l (x l ,y l ), and convert them into points C 1 (x 1 ,y 1 ) and C 2 (x 2 ,y 2 ) in the world coordinate system according to formulas (8)(9), (10)(11). Then the center distance D 1 of the sinking groove is:

[0198]

[0199] Because the line connecting the two centers may not be perpendicular to the axis of the vertical axis, and their x 1 and x 2 may not be equal, there may be an offset between the centers of the upper and lower sinking grooves.

[0200] Step 5. Perform contour fitting on the upper and lower camera lines to determine the equations of the upper and lower outer diameter lines. Take 2 points on the contour-fitted points and convert them into point positions in the world coordinate system through formulas (8)(9), (10)(11), where:

[0201] The upper camera points are denoted as: a u1 (x 1 ,y 1 ) a u2 (x 2 ,y 2 )

[0202] The lower camera points are denoted as: a l1 (x 3 ,y 4 ) a l2 (x 3 ,y 4 )

[0203] Their line equations are:

[0204]

[0205] Since the two lines are not necessarily parallel, use the upper camera point a u1 (x 1 ,y 1 ) to solve the distance to the lower camera line, and then the shaft diameter can be obtained, denoted as D 2 :

[0206] Let the fitting straight line of the following camera be:

[0207] ax + by + c = 0 (14)

[0208] where

[0209]

[0210] Then

[0211]

[0212] It is easy for those skilled in the art to understand that the above is only a preferred embodiment of the present invention and does not limit the present invention. Any modifications, combinations, substitutions, improvements, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A method for detecting the spacing and center distance of the sinking groove by binocular lens image stitching, characterized in that: It is used to measure the spacing and center distance of the sinking grooves of the shaft parts (5) to be measured, and includes two sets of binocular optical lens modules (3) arranged up and down. Each set of binocular optical lens modules (3) includes a camera and a light source symmetrically arranged on both sides of the shaft parts (5) to be measured and coaxially arranged: S1. Based on the calibration plate and the image processing unit, eliminate the radial distortion and tangential distortion of the binocular optical lens module (3) to obtain the calibrated world coordinate system; S2. The upper camera of the binocular optical lens module (3) takes pictures of the sinking grooves of the shaft parts (5) to be measured to obtain the coordinates of the upper sinking groove in the upper camera coordinate system. The lower camera of the binocular optical lens module (3) takes pictures of the sinking grooves of the shaft parts (5) to be measured to obtain the lower sinking groove photos and establish the coordinates of the lower camera coordinate system. Map the upper camera coordinate system and the lower camera coordinate system into the world coordinate system respectively to obtain the coordinates of the upper sinking groove and the lower sinking groove in the world coordinate system; S3. Measure the spacing and center distance of the upper and lower sinking grooves based on the world coordinate system.

2. The method for detecting the spacing and center distance of the sinking groove by binocular lens image stitching according to claim 1, characterized in that: In S1, the specific steps include: S11. Fix the lens and the light source, and adjust the center lines of the single set of lens and the light source to be on a straight line; S12. Adjust the center lines of the two sets of optical lens systems to be collimated. The distance between the two sets of lenses is adjusted according to the length of the calibration plate, so that the midpoints of the boundaries on both sides of the measured object fall on the center line of the optical system as much as possible; S13. Adjust the calibration plate or the binocular vision system to make the pictures taken by the two sets of cameras the clearest; S14. Start the image processing unit, take the upper and lower projection photos of the calibration piece, eliminate the radial distortion of the two lenses, then eliminate the tangential distortion, and calculate the coefficients of the elimination equations of the radial distortion and the tangential distortion.

3. The method for detecting the spacing and center distance of the sinking groove by binocular lens image stitching according to claim 2, characterized in that: In S14, the steps to eliminate distortion include: k 1 ,k 2 is the radial distortion parameter, p 1 ,p 2 is the tangential distortion parameter, r 2 is the known radius of the distortion circle, (x, y) is the coordinate point of the image before distortion, (x^, y^) is the corrected coordinate point. Since (x^, y^) is the checkerboard or dot matrix calibration pattern and its coordinates are known, (x, y) is the coordinate of the actual captured image, and k for each pixel is calculated through (x^, y^) and (x, y) 1 ,k 2 and p 1 ,p 2 parameters. For mirror distortion, substitute the captured image into Formulas 1 and 2 for calculation: x^ = x + x[k 1 (x 2 + y 2 ) 2 + k 2 (x 2 + y 2 ) 2 (1) y^=y+y[k 1 (x 2 +y 2 ) 2 +k 2 (x 2 +y 2 ) 2 (2) For tangential distortion, as shown in formulas 3 and 4: x^ = x + [2p 1 xy + p 2 (r 2 + 2x 2 )] (3) y^ = y + [2p 1 (r 2 + 2y 2 ) + 2p 2 xy] (4).

4. The method for detecting the spacing and center distance of the sinking groove by binocular lens image stitching according to claim 3, characterized in that: In S14, the width W of the undistorted image together with the calibration board a and the length L a are calculated. By edge searching, line segment measurement, and two-dimensional coordinate transformation, etc., the rotation angles θ1, θ2 of each camera relative to the calibration board, the unit pixels μ1, μ2, and the midpoints P1, P2 of the upper and lower image calibration boards are obtained. The P 1 (x p1 , y p1 ) and P 2 (x p2 , y p2 ) coordinates are based on the known size of the calibration board. According to W a , the mapping points of P1 and P2 in the world coordinate system can be obtained as: x wp1 = x wp2 = 0 (5) The calibrated plate pixel width value measured by the upper camera is denoted as W U , and the pixel width value measured by the lower camera is denoted as W L , then the calculation methods of μ1 and μ2 are as follows: Through the above steps, the axis direction, origin of the world coordinate system, and the mapping points of each point in the upper and lower cameras in the world coordinate system can be obtained.

5. The method for detecting the spacing and center distance of the sinking groove by binocular lens image stitching according to claim 1, characterized in that: In S2, For the upper camera, its internal point is (x u , y u ), and the corresponding point in the world coordinate system is (x world , y world ): x world = cosθ 1 μ 1 (x u - x p1 )(8) y world = sinθ 1 μ 1 (y u - y wp1 )(9) For the lower camera, its internal point is (x l , y l ), and the corresponding point in the world coordinate system is (x world , y world ): x world = cosθ 1 μ 2 (x u - x p2 ) (10) y world = cosθ 1 μ 2 (y u + y wp2 ) (11) After the calibration plate image is recalculated and output through the radial distortion and tangential distortion equations with determined coefficients, on this basis, the world coordinate system obtained based on the calibration plate and the center line of the binocular vision system is calculated.

6. The method for detecting the spacing and center distance of the sinking groove by binocular lens image stitching according to claim 1, characterized in that: The specific steps of S3 include, S31. Based on the calibrated camera lens and the frame, place the shaft parts between two groups of lenses, so that one group of lenses can clearly capture the projection of the sunk cutting groove of the shaft parts, and the other group of lenses can clearly capture the projection of the sunk cutting groove on the other side. S32. Use the camera to take 2 photos of the sunk cutting grooves of the shaft parts and input them into the vision processing unit for image calculation. S33. According to the calibrated world coordinate system, the vision processing system first maps and splices the two pictures through the world coordinate system, synthesizes and outputs them into one image. S34. On this spliced image, fit the center of the sinking groove by the least squares method, and find the centers of the upper and lower sinking grooves, denoted as C u (x u , y u ), C l (x l , y l ), and according to the formula x world = cosθ 1 μ 1 (x u - x p1 ) (8) y world = sinθ 1 μ 1 (y u - y wp1 ) (9) x world = cosθ 1 μ 2 (x u - x p2 ) (10) y world = cosθ 1 μ 2 (y u + y wp2 ) (11) Convert to point C in the world coordinate system 1 (x 1 ,y 1 ), C 2 (x 2 ,y 2 ), then the center distance D of the counterbore 1 is: Since the line connecting the centers of the two circles may not be perpendicular to the axis of the vertical axis, its x 1 and x 2 may not be equal, so there may be an offset between the centers of the upper and lower sinking grooves; S35. Perform contour fitting on the straight line of the upper and lower cameras to determine the straight line equations of the upper and lower outer diameters. Take 2 points on the points of the contour fitting, and convert them into the point positions in the world coordinate system through formulas (8)(9), (10)(11), where: The upper camera point is denoted as: a u1 (x 1 , y 1 )a u2 (x 2 , y 2 ) The lower camera point is denoted as: a l1 (x 3 , y 4 )a l2 (x 3 , y 4 ) Its straight line equation is: Since the two straight lines are not necessarily parallel, the upper camera point a is used in the application u1 (x 1 , y 1 ) is used to solve the distance to the lower camera straight line, and then the shaft diameter can be obtained, denoted as D 2 : Suppose the fitting straight line of the lower camera is: ax + by + c = 0 (14) where then 7. The method for detecting the spacing and center distance of the sunk cutting grooves by binocular lens image splicing according to claim 1, characterized in that: It includes a manipulator (1), a measurement system (2), a binocular optical lens module (3), and a manipulator control system (4). The manipulator control system (4) is electrically connected to the manipulator (1), and the binocular optical lens module (3) is connected to the mobile end of the manipulator (1); the binocular optical lens module (3) includes a frame (31) for connecting the manipulator (1), and on the frame (31), there are V-shaped positioning blocks (32) and U-shaped cantilevers (33) arranged at intervals along the axial direction of the shaft parts (5) to be measured. On the U-shaped cantilever (33), there are two groups of shooting units arranged at intervals up and down for shooting the sunk cutting grooves on the shaft parts (5) to be measured. Each shooting unit includes a coaxially arranged camera (34) and a lighting source (35). The camera (34) and the lighting source (35) are symmetrically arranged on both sides of the shaft parts (5) to be measured. The camera (34) is electrically connected to the measurement system (2); the symmetry axis of the V-shaped positioning block (32) coincides with the symmetry axis of the U-shaped cantilever (33).

8. The method for detecting the spacing and center distance of the sunk cutting grooves by binocular lens image splicing according to claim 7, characterized in that: The V-shaped positioning block (32) includes two positioning inclined planes symmetrically arranged with respect to the central axis of the shaft parts (5) to be measured; on the frame (31), there is a quick-change joint for connecting the manipulator (1).

9. The method for detecting the spacing and center distance of the sunk cutting grooves by binocular lens image splicing according to claim 1, characterized in that: It includes a support bench (6) for positioning a shaft-like part (5) to be measured. A three-axis motion unit (8) is arranged beside the support bench (6), and the moving end of the three-axis motion unit (8) is connected with an image acquisition and processing unit (10); the three-axis motion unit (8) includes a fixed gantry (81), a processing unit is arranged on the fixed gantry (81), a first linear module (82) arranged along the axial direction of the shaft-like part (5) to be measured is arranged on the fixed gantry (81), the moving end of the first linear module (82) is connected with a second linear module (83) arranged perpendicular to it, a third linear module (84) arranged along the vertical direction is arranged on the moving end of the second linear module (83), connecting cantilevers (85) are symmetrically arranged on the moving end of the third linear module (84), and two groups of image acquisition and processing units (10) arranged at intervals up and down are arranged on the connecting cantilevers (85). Each image acquisition and processing unit (10) includes a shooting camera (101), a light source (102) and a data processing unit. The shooting camera (101) and the light source (102) are coaxially arranged, the shooting camera (101) is electrically connected with the data processing unit, and the shooting camera (101) and the light source (102) are symmetrically arranged on both sides of the shaft-like part (5) to be measured; a stepping transmission unit (7) for driving it to move along the axial direction of the shaft-like part (5) to be measured is connected to the support bench (6).

10. The method for detecting the spacing and center distance of the sinking groove by binocular lens image stitching according to claim 9, characterized in that: an infrared trigger unit (9) for triggering the camera to take pictures is arranged beside the support bench (6); the fixed gantry (81) includes bases symmetrically arranged on both sides of the support bench (6) and a gantry connected to the two bases.

Images