Calibration method of microstructured light 3D measurement system based on standard sphere

Abstract

This invention discloses a calibration method for a microscopic structured light three-dimensional measurement system based on a standard sphere, belonging to the field of structured light three-dimensional measurement technology. The method includes the following steps: S1, constructing a three-dimensional measurement model based on a triangulation structured light system, and establishing a new world coordinate system according to constraints; S2, constructing the system using a telecentric lens, representing the world coordinate system using camera and projector coordinate systems, and obtaining the three-dimensional coordinate formula based on geometric constraints; S3, deriving the solution method for specific calibration parameters during system calibration based on the special geometric structure of the standard sphere; S4, treating the projector as an inverse camera, and establishing the relationship between camera pixels and projector pixels using the same-point matching method generated by structured light image encoding projection; S5, using the camera to capture a set of horizontal and vertical fringe projection images of the sphere, and obtaining the calibration parameters. This invention only requires acquiring a set of horizontal and vertical fringe projection images to complete the calibration of the entire system, making the operation simple.

Description

Technical Field

[0001] This invention relates to the field of structured light three-dimensional measurement technology, and specifically to a calibration method for a microscopic structured light three-dimensional measurement system based on a standard sphere. Background Technology

[0002] Structured light 3D measurement technology has been widely used in industrial inspection, medical imaging, and defect detection due to its significant advantages such as non-contact operation, high precision, and high efficiency. The principle of structured light 3D measurement is to project light with stripe codes onto the object being measured, and a camera collects the corresponding deformed stripe patterns. After decoding, phase information is extracted, and finally, the three-dimensional coordinates of the object are obtained by calibrating the internal and external parameters of the system.

[0003] Structured light system calibration is a crucial step in achieving 3D measurement. Currently, calibration methods are mainly divided into two categories: phase height method and triangulation method. The phase height method directly establishes a functional relationship between phase difference and height, but this method is limited by geometric constraints, and the height reconstruction error is relatively large when the phase difference is 0. Subsequently, the virtual reference plane was proposed, which creates a virtual reference plane with a known height along the original reference plane, such as the "fast large-range phase unwrapping method based on dual reference planes" disclosed in patent CN 202010248074.2. The virtual reference plane method produces higher reconstruction accuracy throughout the measurement range, but complicates system calibration. The triangulation method establishes a system model including the camera coordinate system, world coordinate system, and projected coordinate system, and achieves triangulation through the transformation relationship between the coordinate systems. In system calibration, the projector is regarded as the "inverse camera," and the projection process is regarded as the reverse process of camera acquisition. At this time, the system calibration can be regarded as the calibration of two cameras. Camera calibration often adopts the Zhang Zhengyou calibration method, which involves photographing a standard calibration board, detecting corner points, and calibrating the camera's intrinsic and extrinsic parameters. This method typically requires multiple calibration images in different poses during calibration, which is cumbersome. It is prone to calibration failure when the depth of field is limited or the calibration board is tilted at a large angle, resulting in poor versatility and lack of universality in some industrial scenarios. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a calibration method for a microstructure light three-dimensional measurement system based on a standard sphere. The calibration of the entire system can be completed by acquiring only one set of projected fringe patterns, and the operation is simple.

[0005] The technical problem to be solved by this invention is achieved by the following technical solution:

[0006] The calibration method for a microscopic structured light three-dimensional measurement system based on a standard sphere includes the following steps:

[0007] S1. Build a three-dimensional measurement model based on a triangulation structured light system, and establish a new world coordinate system according to the constraints.

[0008] The optical axes of camera A and projector B lie in the same plane, their optimal imaging centers coincide, and their vertical coordinates are parallel, i.e., v A ∥v B Choose any plane H perpendicular to the angle bisectors of the optical axes of the two lenses. The intersection points of H with the two optical axes are O′ and O″. The line connecting O′ and O″ is the X-axis, parallel to the vertical coordinate v. A The Y-axis extends outwards, and the Z-axis is the vertical line bisector of the optical axis angle, intersecting O′O″ at O. With O as the origin, a world coordinate system O-XYZ is established, and the angle between the optical axes of camera A and projector B is 2θ.

[0009] S2. Build a system using a telecentric lens, represent the world coordinate system using the camera coordinate system and the projector coordinate system, and obtain the three-dimensional coordinate formula based on the geometric constraints.

[0010] Establish a camera coordinate system O′-x′y′z′ and a projector coordinate system O″-x″y″z″ with O′ and O″ as origins respectively. The x′ axis and x″ axis are on the same straight line with the X axis and have the same direction, while the z′ axis and z″ axis are parallel to the Z axis and have the same direction.

[0011] For any point P in space, let the distance between O′ and O″ be 2l, then the coordinate constraint condition of point P is: Point P is projected onto points C and D on plane H along the optical axes of camera A and projector B, respectively. Geometrically, the world coordinates of point P are: Express the coordinates of point P using the coordinates of the local coordinate systems O′ and O″.

[0012] Because telecentric lenses possess orthographic projection characteristics and low distortion, they can directly describe the physical coordinates of the camera sensor pixels. Let the magnification of the lenses of camera A and projector B be β respectively. A β B According to geometric relationships, the local coordinates (x) i ′,y i (′) and image plane coordinates (u) i ,v i Satisfying between ) Where i = A and B, substituting them into point P, we know that the absolute formula for three-dimensional coordinates is: in, d0 is the system calibration length unit; μ A and μ B These are the sensor pixel sizes for camera A and projector B, respectively; (u A ,vA ) and (u B ,v B Let A and B be the image plane coordinates of camera A and projector B, respectively. The intersection of the optical axis and the sensor is taken as the origin of the reference coordinate system. For the reference coordinate system, the relative coordinates of the 3D reconstruction are:

[0013] As can be seen from the above formula, the system's measurement accuracy can reach the same pixel level and is not affected by the distance l between the two lenses, which reflects the system's microscopic characteristics.

[0014] S3. Based on the special geometric structure of the standard sphere, derive the solution method for specific calibration parameters during the system calibration process.

[0015] Considering installation errors, the optical axes of camera A and projector B are not in the same plane, and their vertical coordinates are not parallel. Error correction is introduced by combining the 3D reconstruction formula.

[0016] Correction for non-coplanarity of optical axes: Y = v A =εv B +d. Where d is the distance that projector B translates along the vertical axis of camera A; ε is a constant related to the relative magnification of the two camera lenses and their relative pixel size.

[0017] Correction for non-parallelism of the ordinate: The intersection of the optical axis and the sensor is W(u0,v0). Taking camera A as the reference, projector B is rotated around the optical axis by an angle α, with the positive direction of rotation along the propagation direction of the optical axis, to obtain... Among them, (u′ B ,v′ B ) represents the pixel coordinates of the image; (u B ,v B Let be the image plane coordinates after the camera has rotated around the optical axis, and then obtain... Wherein, δv is a definite constant, determined as the camera is installed. Further, we obtain... In summary, the parameters that need to be calibrated in the three-dimensional coordinate formula are κ, θ, ε, α and δv0.

[0018] ε, α, and δv0 can be obtained by taking three non-collinear object points P. i (X i ,Y i Z i ) Forming equations Perform the calculation. Where, (Δu) i ′,Δv i ′), i=1,2, representing P i Relative to the pixel coordinates of P0, Substituting these values ​​into the equation allows us to solve for δv0 and ε.

[0019] To solve for κ and θ, we construct the equation using a sphere, employing a standard sphere approach. Let the radius of the standard sphere be R, and using the formula for the circumcenter coordinates of a tetrahedron, we take four points P on the sphere. i (i = 0, 1, 2, 3), the coordinates of the sphere's center are... Among them, D and D i (i = 1, 2, 3) are all determinants. According to the formula for the external center coordinates of a tetrahedron, we know that Tetrahedron vertex P i (i = 0, 1, 2, 3) should lie on a unit sphere, satisfying (X i -X C ) 2 +(Y i -Y C ) 2 +(Z i -Z C ) 2 =1; Choose a sphere with a different value than P. i The fifth coordinate point P4(X4,Y4,Z4) of (i=0,1,2,3) also satisfies the unit sphere condition, resulting in (X4-X C ) 2 +(Y4-Y C ) 2 +(Z4-Z C ) 2 =(X i -X C ) 2 +(Y i -Y C ) 2 +(Z i -Z C ) 2 κ and θ can be solved from the two equations.

[0020] S4. Treat the projector as a reverse camera and project a stripe pattern onto the object. Decode the absolute phase using the phase-shifting method. The phase of the same object point is the same. Use the same point matching method generated by structured light image encoding projection to establish the relationship between camera pixels and projector pixels. Where p is the projector pixel; c is the camera pixel; W is the field width of the coded stripe; and Φ is the absolute phase, ranging from (0, 2π).

[0021] S5. Use a camera to capture a set of horizontal and vertical stripe projection images of the sphere, decode to obtain the absolute phase, and solve for its coordinates based on the relationship between camera pixels and projector pixels; obtain object points on the sphere as required, substitute them into the calibration parameter solution formula, and solve for the calibration parameters κ, θ, ε, α and δv0. Substitute the obtained calibration parameters into the three-dimensional coordinate formula to complete the calibration of the entire system.

[0022] The beneficial effects of this invention are as follows: Compared with the prior art, the calibration method for the structured light three-dimensional measurement system provided by this invention has the following advantages:

[0023] 1. The calibration of the entire system can be completed by taking only one set of projected fringe images, which reduces the acquisition of calibration images and is very convenient;

[0024] 2. The calibration of the entire system is completed by photographing the small ball, reducing the number of parameters that need to be calibrated;

[0025] 3. The spherical surface of the small ball is more likely to acquire effective information than the calibration board, which increases the probability of successful calibration when the depth of field is limited. Attached Figure Description

[0026] Figure 1 A coordinate system diagram illustrating the geometric principles of a structured light system;

[0027] Figure 2 A diagram of the reference coordinate system for the measurement system;

[0028] Figure 3 These are the calibration ball images and absolute phase images collected during the calibration process;

[0029] Figure 4 This is a 3D reconstruction of a standard sphere. Detailed Implementation

[0030] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below with reference to specific embodiments and illustrations.

[0031] Equipment preparation: camera, projector, telecentric lens, fixed bracket, calibration ball (r = 4.9991 mm).

[0032] Example 1

[0033] S1, Build as follows Figure 1 The three-dimensional measurement model based on the triangulation structured light system shown is used to establish a new world coordinate system according to the constraints.

[0034] The optical axes of camera A and projector B lie in the same plane, their optimal imaging centers coincide, and their vertical coordinates are parallel, i.e., v A ∥v B Choose any plane H perpendicular to the angle bisectors of the optical axes of the two lenses. The intersection points of H with the two optical axes are O′ and O″. The line connecting O′ and O″ is the X-axis, parallel to the vertical coordinate v. AThe Y-axis extends outwards, and the Z-axis is the vertical line bisector of the optical axis angle, intersecting O′O″ at O. With O as the origin, a world coordinate system O-XYZ is established, and the angle between the optical axes of camera A and projector B is 2θ.

[0035] S2. Build a system using a telecentric lens, represent the world coordinate system using the camera coordinate system and the projector coordinate system, and obtain the three-dimensional coordinate formula based on the geometric constraints.

[0036] Establish a camera coordinate system O′-x′y′z′ and a projector coordinate system O″-x″y″z″ with O′ and O″ as origins respectively. The x′ axis and x″ axis are on the same straight line with the X axis and have the same direction, while the z′ axis and z″ axis are parallel to the Z axis and have the same direction.

[0037] Figure 2 Therefore Figure 1 In the diagram, O is the origin of the measurement system's reference coordinate system. For any point P in space, let the distance between O′ and O″ be 2l, then the coordinate constraints of point P are: Point P is projected onto points C and D on plane H along the optical axes of camera A and projector B, respectively. Geometrically, the world coordinates of point P are: Express the coordinates of point P using the coordinates of the local coordinate systems O′ and O″.

[0038] Because telecentric lenses possess orthographic projection characteristics and low distortion, they can directly describe the physical coordinates of the camera sensor pixels. Let the magnification of the lenses of camera A and projector B be β respectively. A β B According to geometric relationships, the local coordinates (x) i ′,y i (′) and image plane coordinates (u) i ,v i Satisfying between ) Where i = A and B, substituting them into point P, we know that the absolute formula for three-dimensional coordinates is: in, d0 is the system calibration length unit; μ A and μ B These are the sensor pixel sizes for camera A and projector B, respectively; (u A ,v A ) and (u B ,v B Let A and B be the image plane coordinates of camera A and projector B, respectively. The intersection of the optical axis and the sensor is taken as the origin of the reference coordinate system. For the reference coordinate system, the relative coordinates of the 3D reconstruction are:

[0039] As can be seen from the above formula, the system's measurement accuracy can reach the same pixel level and is not affected by the distance l between the two lenses, which reflects the system's microscopic characteristics.

[0040] S3. Based on the special geometric structure of the standard sphere, derive the solution method for specific calibration parameters during the system calibration process.

[0041] Considering installation errors, the optical axes of camera A and projector B are not in the same plane, and their vertical coordinates are not parallel. Error correction is introduced by combining the 3D reconstruction formula.

[0042] Correction for non-coplanarity of optical axes: Y = v A =εv B +d. Where d is the distance that projector B translates along the vertical axis of camera A; ε is a constant related to the relative magnification of the two camera lenses and their relative pixel size.

[0043] Correction for non-parallelism of the ordinate: The intersection of the optical axis and the sensor is W(u0,v0). Taking camera A as the reference, projector B is rotated around the optical axis by an angle α, with the positive direction of rotation along the propagation direction of the optical axis, to obtain... Among them, (u′ B ,v′ B ) represents the pixel coordinates of the image; (u B ,v B Let be the image plane coordinates after the camera has rotated around the optical axis, and then obtain... Wherein, δv is a definite constant, determined as the camera is installed. Further, we obtain... In summary, the parameters that need to be calibrated in the three-dimensional coordinate formula are κ, θ, ε, α and δv0.

[0044] ε, α, and δv0 can be obtained by taking three non-collinear object points P. i (X i ,Y i Z i ) Forming equations Perform the calculation. Where, (Δu) i ′,Δv i ′), i=1,2, representing P i Relative to the pixel coordinates of P0, Substituting these values ​​into the equation allows us to solve for δv0 and ε.

[0045] To solve for κ and θ, we construct the equation using a sphere, employing a standard sphere approach. Let the radius of the standard sphere be R, and using the formula for the circumcenter coordinates of a tetrahedron, we take four points P on the sphere. i (i = 0, 1, 2, 3), the coordinates of the sphere's center are... Among them, D and D i (i = 1, 2, 3) are all determinants. According to the formula for the external center coordinates of a tetrahedron, we know that Tetrahedron vertex P i (i = 0, 1, 2, 3) should lie on a unit sphere, satisfying (X i -X C ) 2 +(Y i -Y C ) 2 +(Z i -Z C ) 2 =1; Choose a sphere with a different value than P. i The fifth coordinate point P4(X4,Y4,Z4) of (i=0,1,2,3) also satisfies the unit sphere condition, and we can obtain (X4-X C ) 2 +(Y4-Y C ) 2 +(Z4-Z C ) 2 =(X i -X C ) 2 +(Y i -Y C ) 2 +(Z i -Z C ) 2 Its spatial coordinates are homogeneous. Since the coordinates are proportional to κ, during calibration calculations, κ can be set to 1 to obtain the value of θ. Finally, the result is obtained from... κ is obtained. At this point, all calibration parameters have been solved.

[0046] S4. Treat the projector as a reverse camera and project a stripe pattern onto the object. Decode the absolute phase using the phase-shifting method. The phase of the same object point is the same. Use the same point matching method generated by structured light image encoding projection to establish the relationship between camera pixels and projector pixels. Where p is the projector pixel; c is the camera pixel; W is the field width of the coded stripe; and Φ is the absolute phase, ranging from (0, 2π).

[0047] S5. Using a computer-controlled camera, capture a set of horizontal and vertical projection fringe patterns of the sphere, decode them to obtain the absolute phase, and compare the calibrated sphere captured by the camera with the decoded horizontal and vertical absolute phase patterns as shown below. Figure 3 As shown. The coordinates of the camera and projector pixels are calculated based on their relationship. Object points are obtained on the sphere as required, and substituted into the calibration parameter calculation formula to solve for the calibration parameters κ, θ, ε, α, and δv0. The obtained calibration parameters are then substituted into the three-dimensional coordinate formula to complete the calibration of the entire system.

[0048] Traditional calibration methods are typically divided into camera calibration and projector calibration. Camera calibration often employs the Zhang Zhengyou calibration method, which involves photographing a standard calibration board (chessboard or dot diagram), detecting corner points, and calibrating the camera's intrinsic and extrinsic parameters. Projector calibration primarily establishes the relationship between camera pixels and projector pixels, ensuring that the phase of the same object point is the same for both, and that the camera's corner coordinates can be mapped to the projector coordinates. After calibrating the intrinsic parameters of the camera and projector, a new world coordinate system is established, and the entire system calibration is completed through rotation and translation. Ten repeated radius fitting experiments were conducted on a calibration ball (r = 4.9991 mm) using both the calibration method of this invention and the traditional calibration method, and the root mean square error (RMS) of the point cloud fitting was calculated. The results are shown in Table 1.

[0049] Table 1

[0050]

[0051] As shown in Table 1, the average fitted radius of the reconstructed sphere using the traditional calibration method is 4.454945 mm, with a reconstruction accuracy of approximately 50 μm and an average RMS value of approximately 0.050 for the point cloud fitting. In contrast, the average fitted radius of the reconstructed sphere using the calibration method of this invention is 4.998746 mm, with a reconstruction accuracy of approximately 4 μm and an average RMS value of approximately 0.029 for the point cloud fitting. This demonstrates that the system accuracy of the calibration method of this invention is an order of magnitude higher than that of the traditional calibration method, and the quality of the acquired point cloud is also significantly improved. Figure 4 To reconstruct the three-dimensional point cloud map of the calibration sphere after system calibration using the method described in this invention, the surface is smooth with no significant deformation or loss.

[0052] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A calibration method for a three-dimensional microscopic structured light measurement system based on a standard spherical surface, characterized in that, Includes the following steps: S1. Construct a three-dimensional measurement model based on a triangulation structured light system, and establish a new world coordinate system according to the constraints. S2. Build a system using a telecentric lens, represent the world coordinate system using the camera coordinate system and the projector coordinate system, and obtain the three-dimensional coordinate formula based on the geometric constraints. S3. Based on the special geometric structure of the standard sphere, derive the solution method for specific calibration parameters during the system calibration process; S4. Treat the projector as an inverse camera and use the same point matching method generated by structured light image coding projection to establish the relationship between camera pixels and projector pixels. S5. Use a camera to take a set of horizontal and vertical stripe projection images of the sphere, and obtain the calibration parameters according to steps S2 and S3 to complete the calibration of the overall system. The constraints for establishing the world coordinate system in step S1 specifically include: the optical axes of camera A and projector B are in the same plane, the optimal imaging centers coincide, and the vertical coordinates are parallel, i.e., v A ||v B Choose any plane H perpendicular to the angle bisectors of the optical axes of the two lenses. The intersection points of H with the two optical axes are O′ and O″. The line connecting O′ and O″ is the X-axis, parallel to the vertical coordinate v. A The Y-axis extends outwards, and the Z-axis is the vertical line that bisects the angle of the optical axis. It intersects O′O″ at O. With O as the origin, a world coordinate system O-XYZ is established. The angle between the optical axes of camera A and projector B is 2θ. The specific steps for obtaining the three-dimensional coordinate formula based on geometric constraints in step S2 are as follows: Establish a camera coordinate system O′-x′y′z′ and a projector coordinate system O″-x″y″z″ with O′ and O″ as origins respectively. The x′ axis and x″ axis are on the same straight line with the X axis and have the same direction, while the z′ axis and z″ axis are parallel to the Z axis and have the same direction. For any point P in space, let the distance between O′ and O″ be 2l, then the coordinate constraints of point P are as follows: Point P is projected onto points C and D on plane H along the optical axes of camera A and projector B, respectively. Geometrically, the world coordinates of point P are: Express the coordinates of point P using the coordinates of the local coordinate systems O′ and O″. Let the magnification of the lenses of camera A and projector B be β respectively. A β B According to geometric relationships, the local coordinates (x) i ′,y i (′) and image plane coordinates (u) i ,v i Satisfying between ) Where i = A and B, substituting them into point P, we know that the absolute formula for three-dimensional coordinates is: in, d0 is the system calibration unit of length; μ A and μ B These are the sensor pixel sizes for camera A and projector B, respectively; (u A ,v A ) and (u B ,v B The coordinates of the image planes of camera A and projector B are given by ( ). The intersection of the optical axis and the sensor is taken as the origin of the reference coordinate system. For the reference coordinate system, the relative coordinates of the 3D reconstruction are ( ). The method for solving the calibration parameters in step S3 specifically includes the following steps: Correction for non-coplanarity of optical axes: Y = v A =εv B +d; where d is the distance that projector B translates along the vertical axis of camera A; ε is a constant related to the relative magnification of the two camera lenses and their relative pixel size; Correction for non-parallelism of the ordinate: The intersection of the optical axis and the sensor is W(u0,v0). Taking camera A as the reference, projector B is rotated around the optical axis by an angle α, with the positive direction of rotation along the propagation direction of the optical axis, to obtain... Among them, (u′ B ,v′ B ) represents the pixel coordinates of the image; (u B ,v B Let be the image plane coordinates after the camera has rotated around the optical axis, and then obtain... Where δv is a definite constant as the camera is installed; further, we obtain By taking three non-collinear points P i (X i ,Y i Z i ) Forming equations Calculate ε, α, and δv0; where, (Δu i ′,Δv i ′), i = 1, 2, representing P i Relative to the pixel coordinates of P0, Substituting these values ​​into the equations allows us to solve for δv0 and ε. Let the radius of the standard sphere be R, and use the formula for the external center coordinates of a tetrahedron to select four points P on the surface of the sphere. i (i = 0, 1, 2, 3), the coordinates of the sphere's center are... Among them, D and D i (i = 1, 2, 3) are all determinants. According to the formula for the external center coordinates of a tetrahedron, we know that Tetrahedron vertex P i (i = 0, 1, 2, 3) should lie on a unit sphere, satisfying (X i -X C ) 2 +(Y i -Y C ) 2 +(Z i -Z C ) 2 =1; Choose a sphere with a different value than P. i The fifth coordinate point P4(X4,Y4,Z4) of (i=0,1,2,3) is obtained, which gives (X4-X C ) 2 +(Y4-Y C ) 2 +(Z4-Z C ) 2 =(X i -X C ) 2 +(Y i -Y C ) 2 +(Z i -Z C ) 2 Solve for κ and θ.

2. The calibration method for a microscopic structured light three-dimensional measurement system based on a standard spherical surface according to claim 1, characterized in that, The relationship between camera pixels and projector pixels in step S4 is as follows: Where p is the projector pixel; c is the camera pixel; W is the field width of the coded stripe; and Φ is the absolute phase, ranging from (0, 2π).

3. The calibration method for a three-dimensional microscopic structured light measurement system based on a standard spherical surface according to claim 1, characterized in that, The calibration of the overall system in step S5 specifically includes the following steps: using a camera to capture a set of horizontal and vertical stripe projection images of the sphere, decoding to obtain the absolute phase, and solving its coordinates based on the relationship between camera pixels and projector pixels; acquiring object points on the sphere as required, substituting them into the calibration parameter solution formula, and solving for the calibration parameters κ, θ, ε, α, and δv0; and substituting the obtained calibration parameters into the three-dimensional coordinate formula to complete the calibration of the overall system.

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