CN111091599A - Multi-camera-projector system calibration method based on sphere calibration object - Google Patents
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Abstract
The invention discloses a calibration method of a multi-camera-projector system based on a sphere calibration object. The method comprises the following steps: 1) extracting the outline of the sphere imaged under the camera plane and fitting the outline into an elliptic curve; 2) acquiring an absolute phase value of each pixel of the camera by using a structured light method, and acquiring an imaging curve of a sphere under a projector by using a pole-polar line relation; 3) calibrating an internal parameter matrix according to more than 3 curves corresponding to the camera and the projector respectively; 4) and (4) calculating the coordinates of the sphere center under each device coordinate system, and unifying all the devices under the same world coordinate system by using a global registration method. The experimental results of the method in the embodiment prove the feasibility and the accuracy of the method.
Description
Technical Field
The invention relates to a multi-camera multi-projector simultaneous calibration technology, in particular to a multi-camera-projector system calibration method based on a sphere calibration object, and belongs to the technical field of optical precision measurement.
Background
With the increasing demand of industrial measurement, the optical three-dimensional measurement is receiving more and more attention due to its simple operation and accurate data. Among many optical three-dimensional measurement techniques, Fringe Projection Profilometry (FPP) has been widely studied and used due to its outstanding advantages of high speed, high accuracy and large field of view. In general, a structured light measurement system based on the FPP principle differs from conventional stereo vision in that it replaces one of the cameras with a digital projector. The projector is used for projecting the coded pattern template to the object to be measured, the camera shoots the patterns on the object, the corresponding relation between the camera pixel and the projector pixel is established through the corresponding decoding algorithm, and then the three-dimensional shape of the target object is reconstructed by combining the calibration parameters and utilizing a trigonometry method. For measurement systems of such camera/projector pairs, proper calibration of each component is crucial for accurately reconstructing the three-dimensional shape.
Calibration of such structured light systems is further complicated by the use of projectors involved. The classical method of comparison is to regard the projector as a reverse camera, obtain the absolute phase value by the phase shift method to establish the mapping of the pixel level between the camera and the projector, and then calibrate the system by the general camera calibration method. However, this method requires a planar calibration plate, which cannot be guaranteed to be "seen" by the system at multiple angles when multiple cameras and projectors are used, and thus is hardly suitable for calibrating a multi-camera-projector system. In addition, if a plurality of plane calibration plates form a cubic calibration object, on one hand, the assembly precision is not sufficient, and on the other hand, because the position and posture of the calibration object need to be changed continuously in the calibration process, the number of planes of the calibration object shot by the camera each time is not uniform, so that the correspondence of the mark points on each plane is difficult to determine, and the calibration fails.
Disclosure of Invention
In view of the above technical problems, the present invention provides a calibration method for a multi-camera-projector system based on a sphere calibration object. The method takes advantage of the isotropy of the sphere's visibility at any angle, and allows simultaneous cameras and projectors in the system by projecting the sphere's outline onto the respective camera and projector phase planes.
The invention adopts the following technical scheme for solving the technical problems:
the invention provides a calibration method of a multi-camera-projector system based on a sphere calibration object, in the multi-camera-projector system, a single camera and a single projector form a structured light measuring unit, a plurality of structured light measuring units in the multi-camera-projector system are annularly placed by taking a measuring area as a center, and the optical axes of each camera and each projector are aligned to the measuring area; each structured light measuring unit works independently, and the projection breadth of the projector in each structured light measuring unit covers the shooting breadth of the camera;
the calibration method specifically comprises the following steps:
step 1, placing a sphere calibration object in a measurement area of a multi-camera-projector system, starting each structured light measurement unit to sequentially perform pattern projection and shooting on the sphere calibration object, and respectively obtaining projection curves of the sphere calibration object under each camera and each projector;
step 2, changing the position of the sphere calibration object in the central measurement area and repeatedly executing the step 1 to obtain at least 3 different projection curves in respective phase planes of each camera and each projector, and obtaining the internal parameters of each camera and each projector according to the projection curves;
and 3, under each camera/projector coordinate system, calculating the coordinates of the sphere center of the sphere calibration object under the coordinate system by using the following formula:
wherein α is tan (θ/2), θ is a cone angle, K is an internal parameter of the camera/projector, r is a radius of the sphere calibration object, and o is a projection coordinate of a sphere center of the sphere calibration object;
and 4, matching the coordinates of the center of sphere under each camera/projector coordinate system by using a global matching method to obtain a relative rotation matrix and a relative translation vector between the cameras/projectors, and finally unifying all the cameras and the projectors under the same world coordinate system to finish calibration.
As a further technical solution of the present invention, the method for obtaining the projection curve of the sphere calibration object under each camera and projector in step 1 specifically comprises:
step 1.1, shooting a sphere calibration object through a camera in each structured light measuring unit, extracting a sub-pixel level outer contour of the sphere calibration object imaged on the camera, and fitting the sub-pixel level outer contour into an elliptic curve by using a least square method, wherein the elliptic curve is a projection curve of the sphere calibration object under the camera;
step 1.2, the projector in each structured light measurement unit sequentially projects a group of phase shift sine stripes and Gray code patterns to the sphere calibration object, the phase shift sine stripes and the Gray code patterns are shot by the corresponding camera, the absolute phase value of each pixel of the camera is solved by a phase expansion method, the antipodal geometric relation between the camera and the projector is calculated by phase mapping by using an eight-point method, and the pole coordinates in the phase plane of the camera and the phase plane of the projector are obtained;
step 1.3, the absolute phase value of each camera pixel solved in step 1.2 is used as the gray value of an image to obtain a phase diagram, a phase value-free area caused by the fact that light of a projector is shielded in an elliptic curve fitted in step 1.1 is positioned in the phase diagram, the outer boundary of the phase value-free area, which is deviated to one side of the center of the elliptic curve, is extracted, the outer boundary is fitted into a quadratic curve, the quadratic curve and the elliptic curve are intersected at two points, and the two points are two image points of the intersection point of the apparent contour line in the plane of the camera;
step 1.4, corresponding the two image points in step 1.3 to the plane of the projector through the absolute phase values thereof to obtain two intersection points iP1,iP2On the straight line l ═ iP1×iP2Coordinate e of pole in the plane of the projectorrAnd projection curve C of sphere calibration object under projectorPSatisfy l ═ CP·erAnd i isP1,iP2Is located at CPFrom the above, the projection curve C of the sphere calibration object under the projector is obtainedP。
As a further technical scheme of the invention, the internal parameter K of the camera/projector in the step 2 is as follows:
wherein f isu,fvFocal length in the u and v axis directions, s is the offset between the u and v axes, respectively, (u0,v0) Is the phase plane principal point coordinate.
As a further technical scheme of the invention, in the step 2, the intrinsic parameters of each camera and each projector are obtained by applying a bi-tangential, semi-definite programming or orthogonal constraint method.
As a further technical scheme of the invention, the value of α in the step 3 is represented by the formula KTThe characteristic value of CK is uniquely determined, and C is a camera projection curve.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects: the invention overcomes the technical bottleneck that the traditional plane calibration method cannot be suitable for the calibration of a multi-camera-projector system, so that the cameras and the projectors at multiple angles can be calibrated simultaneously. The method is simple to operate, calibration can be completed only by using the spherical calibration object, and other additional equipment and steps are not needed. In addition, once the cameras and the projectors under a plurality of visual angles are calibrated, the point clouds reconstructed by the cameras and the projectors can be automatically spliced without additional algorithms, so the calibration method provided by the invention has important significance for constructing a multi-camera-projector rapid measurement system, and the rapid measurement system calibrated by the method can measure the multi-angle three-dimensional shapes of moving objects in real time and splice the multi-angle three-dimensional shapes into full-view three-dimensional shapes in real time
Drawings
FIG. 1 is a schematic view of the imaging of a sphere under a camera-projector system;
FIG. 2 is a schematic view of a geometric relationship of projection imaging in two phase planes at an intersection point of contour lines viewed from two viewing angles;
FIG. 3 is a schematic diagram of the pole-pole relationship in the right imaging plane;
fig. 4 shows a system formed by calibrating 4 camera-projector pairs with a sphere and a reconstruction result thereof, wherein (a) is the system formed by 4 camera-projector pairs, and (b) is the reconstruction result of 4 point clouds at multiple angles.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings:
a multi-camera multi-projector system configuration and model description:
the invention combines a single camera and a single projector into a structured light measuring unit, and the projection breadth of the projector needs to cover the breadth shot by the camera. Each measuring unit works independently, and the three-dimensional reconstruction can be carried out on the area covered by each measuring unit. A plurality of measurement cells are annularly disposed about a central measurement region, with the optical axis of each device being substantially aligned with the central measurement region.
In the present invention, we treat the projector as an inverse camera and both use the pinhole model to describe the parametric model of the camera and projector. The parameters of each device are thus represented by the projected matrix P ═ K R | t. Wherein,
k is an internal parameter of the device and comprises a focal length f in the u and v axis directionsu,fvDegree of offset s between the u, v axes, and phase plane principal point coordinates (u)0,v0). R, t represent the rotation matrix and translation vector, respectively, from the device coordinate system to the world coordinate system.
Second, sphere projection extraction of projector plane
Fig. 1 is a schematic diagram of the imaging of a sphere in a structured light measurement unit (comprising a camera and a projector), and from the knowledge of the projection geometry, the image of the sphere on the phase plane of the camera is an ellipse. The outer contour of the ellipse can be fitted to a quadratic curve whose matrix representation is denoted CC. The outer contour is formed by the apparent contour line gamma of the surface of the sphereCFormed by projection through a small hole. Since the imaging of the sphere on the camera can be obtained directly by shooting, its imaging on the projector cannot be obtained directly. And as shown in fig. 1, the profile C of the same ball imaged in the camera and projectorC,CPIs composed of different apparent contour lines gammaC,ΓPThe projections are generated, and a direct corresponding relation cannot be established between the projections, so that the traditional phase mapping cannot be applied to obtain the imaging curve of the sphere under the projector.
The invention derives the projection curve of the sphere on the plane of the projector from the relation between the epipolar geometry and the imaging curve, and the specific steps are as follows:
step 2.1: firstly, a ball is shot through a camera, a sub-pixel level outer contour of the ball imaged on the camera is extracted, and the sub-pixel level outer contour is fitted into an elliptic curve C by using a least square methodC。
Step 2.2: a set of phase shifted sinusoidal fringes and gray code patterns are projected onto the sphere in sequence using a projector and captured by a camera. The absolute phase value of each pixel of the camera is solved through a phase unwrapping method.
The above phase unwrapping method calculates an absolute phase value of each pixel, and each pixel in the projector has a preset absolute phase value. The pixels of the camera and the pixels of the projector have the same phase value indicating that they are corresponding points. The corresponding pixel points between the camera and the projector can be known through the phase mapping, so that the epipolar geometric relationship is further calculated.
And then calculating the epipolar geometrical relationship between the camera and the projector by phase mapping by using an eight-point method to obtain the pole coordinates in the two phase planes.
Step 2.3: solving the absolute phase value of each camera pixel to be used as the gray value of the image to obtain a phase diagram, and positioning an elliptic curve C in the phase diagramCThe area without phase value caused by the fact that projector light is blocked (a certain viewing angle difference exists between the camera and the projector, so that a certain part of area on a sphere shot by the camera cannot be irradiated by the projector light, and therefore the area has no phase value). Extracting the deviation ellipse C of the regionCThe outer boundary of one side of the center and fitting into a quadratic curve, which is in accordance with the elliptic curve CCIntersecting at two points. As known from the related geometric knowledge, the two points are the apparent contour line gammaC,ΓPThe image point of the intersection point in the camera plane is shown in fig. 2.
Step 2.4: two image points are corresponding to the plane of the projector through absolute phase values (sub-pixel points are obtained through interpolation of pixel points with effective phase values in neighborhoods), and an intersection point i is obtainedP1,iP2As shown in fig. 3. Assuming the projector is placed to the right of the camera, the coordinates of the right pole in the plane of the projectorIs erThe two intersection points obtained by mapping are iP1,iP2. From iP1,iP2Two points determine a straight line iP1×iP2. It is easy to prove that the straight line and the sphere form an image C under the projectorPAnd pole erSatisfy pole-pole relationship, i.e. pole-pole relationship
l＝CP·er(2)
Note that the curves, lines, and points herein are all expressed using homogeneous coordinates.
Wherein iP1,iP2And pole erIs connected with the curve CPTangent and the tangent point is iP1,iP2. Because of curve CPWith 5 unknowns, equation (2) can provide information about CPOf 3 constraints, while iP1,iP2Are respectively located at CPTwo other independent constraints are provided, so curve CPAn analytical solution can be obtained.
Three, multi-camera-projector system calibration
And after the imaging curve of the sphere under the projector is obtained according to the content, the traditional sphere method can be used for calibrating the parameters. In general, an imaging formula of a sphere Q with radius r and sphere center at coordinate a under the pinhole model can be expressed as,
wherein C is*,Q*Respectively, the dual form of the camera projection curve C and the sphere Q, which are their respective inverses in the expression. The world coordinate system is set to coincide with the camera coordinate system, so the above formula is finally simplified to
βC*＝KKT-ooT(4)
The parameter β is a scale factor, K is a device intrinsic parameter matrix, and o is a projection coordinate of the center of sphere (the projection here refers to a point in space projected to a certain point in the phase plane of the camera/projector, and the point in the phase plane is a space point projection coordinate).
The calibration method comprises the following specific steps:
step 3.1: and placing the calibration ball in a measurement area of a multi-camera-projector system, starting each measurement unit to sequentially perform pattern projection and shooting on the ball, and respectively obtaining the projection curves of the ball under each camera and each projector according to the steps of the previous ball projection extraction.
Step 3.2: step 3.1 is executed by changing the position of the calibration ball a plurality of times. Each camera and projector at least obtain 3 different projection curves in respective phase planes, and the internal parameters K of respective devices are obtained by the projection curves by applying methods such as double tangent, semi-definite programming or orthogonal constraint and the like.
Step 3.3: in each device coordinate system, the coordinates of the sphere center in the device coordinate system can be obtained by using the formula (5).
Where α is tan (θ/2), θ is the cone angle in fig. 1, and α can be expressed by the formula KTThe characteristic value of CK is uniquely determined. Since multiple positions of the sphere are transformed, a set of sphere center coordinates can be obtained for each device coordinate system.
Step 3.4: and matching the sphere center coordinates under each device coordinate system by using a global matching method to obtain relative rotation matrixes and relative translation vectors between the devices, and finally unifying all cameras and projectors under the same world coordinate system to finish calibration.
Two embodiments of the present invention for calibrating a single camera-projector system and a multiple camera-projector system are illustrated, as follows:
example 1: calibrating a single camera-projector system
Step 1: four matte ceramic balls of 50.80mm diameter were mounted on a fixed support and placed in the common field of view of the camera and projector. In this embodiment, an 8-step phase shift method is adopted, and corresponding fringes and gray code patterns are projected to a sphere according to the number of phase shift steps, and a phase diagram is generated by phase-decoding.
Step 2: extracting the outer contours of four balls by using a camera picture, and respectively fitting into 4 elliptic curves C by applying a least square methodC(ii) a Simultaneously applying phase diagram and pole-pole line relation to obtain elliptic curve C of four balls under projectorP。
And step 3: and (3) applying an orthogonal constraint method to the two groups of curves under the camera and the projector to obtain respective internal parameter matrixes K.
And 4, step 4: and (3) solving the positions of the 4 balls under the coordinate systems of the camera and the projector respectively, and registering the two point sets by using a rigid body transformation method to obtain a relative rotation matrix and a translation vector between the camera and the projector so as to finish calibration.
Example 2: calibrating a multi-camera-projector system
Step 1: 4 structured light measuring units consisting of a camera and a projector are placed around the measuring area.
Step 2: to avoid the blocking of spheres from each other that may occur at certain viewing angles when multiple spheres are used simultaneously, only one matt ceramic sphere of 50.80mm diameter is used in this example and placed in the measurement field of view.
And step 3: and sequentially starting the measuring units to scan the ball.
And 4, step 4: and (3) changing the position of the sphere for multiple times, and repeating the step (3) until each device obtains more than 3 projection curves.
And 5: and calibrating the internal parameters of each device by using the projection curve under each device.
And 4, step 4: and (3) solving the positions of the sphere center of the sphere under the coordinate systems of the cameras and the projectors under each position, simultaneously registering all the point sets by using a global registration method, obtaining relative rotation matrixes and translation vectors between all the cameras and the projectors, unifying all the devices under the same coordinate system, and finishing calibration.
The system consisting of 4 camera-projector pairs is calibrated by using the sphere shown in fig. 4 (a), and the reconstruction result of 4 point clouds at multiple angles is obtained as shown in fig. 4 (b).
The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can understand that the modifications or substitutions within the technical scope of the present invention are included in the scope of the present invention, and therefore, the scope of the present invention should be subject to the protection scope of the claims.
Claims (5)
1. A calibration method of a multi-camera-projector system based on a sphere calibration object is characterized in that in the multi-camera-projector system, a single camera and a single projector form a structured light measuring unit, a plurality of structured light measuring units in the multi-camera-projector system are annularly arranged by taking a measuring area as a center, and the optical axes of each camera and each projector are aligned with the measuring area; each structured light measuring unit works independently, and the projection breadth of the projector in each structured light measuring unit covers the shooting breadth of the camera;
the calibration method specifically comprises the following steps:
step 1, placing a sphere calibration object in a measurement area of a multi-camera-projector system, starting each structured light measurement unit to sequentially perform pattern projection and shooting on the sphere calibration object, and respectively obtaining projection curves of the sphere calibration object under each camera and each projector;
step 2, changing the position of the sphere calibration object in the central measurement area and repeatedly executing the step 1 to obtain at least 3 different projection curves in respective phase planes of each camera and each projector, and obtaining the internal parameters of each camera and each projector according to the projection curves;
and 3, under each camera/projector coordinate system, calculating the coordinates of the sphere center of the sphere calibration object under the coordinate system by using the following formula:
wherein α is tan (θ/2), θ is a cone angle, K is an internal parameter of the camera/projector, r is a radius of the sphere calibration object, and o is a projection coordinate of a sphere center of the sphere calibration object;
and 4, matching the coordinates of the center of sphere under each camera/projector coordinate system by using a global matching method to obtain a relative rotation matrix and a relative translation vector between the cameras/projectors, and finally unifying all the cameras and the projectors under the same world coordinate system to finish calibration.
2. The calibration method of a multi-camera-projector system based on a sphere calibration object as claimed in claim 1, wherein the method for obtaining the projection curve of the sphere calibration object under each camera and projector in step 1 comprises:
step 1.1, shooting a sphere calibration object through a camera in each structured light measuring unit, extracting a sub-pixel level outer contour of the sphere calibration object imaged on the camera, and fitting the sub-pixel level outer contour into an elliptic curve by using a least square method, wherein the elliptic curve is a projection curve of the sphere calibration object under the camera;
step 1.2, the projector in each structured light measurement unit sequentially projects a group of phase shift sine stripes and Gray code patterns to the sphere calibration object, the phase shift sine stripes and the Gray code patterns are shot by the corresponding camera, the absolute phase value of each pixel of the camera is solved by a phase expansion method, the antipodal geometric relation between the camera and the projector is calculated by phase mapping by using an eight-point method, and the pole coordinates in the phase plane of the camera and the phase plane of the projector are obtained;
step 1.3, the absolute phase value of each camera pixel solved in step 1.2 is used as the gray value of an image to obtain a phase diagram, a phase value-free area caused by the fact that light of a projector is shielded in an elliptic curve fitted in step 1.1 is positioned in the phase diagram, the outer boundary of the phase value-free area, which is deviated to one side of the center of the elliptic curve, is extracted, the outer boundary is fitted into a quadratic curve, the quadratic curve and the elliptic curve are intersected at two points, and the two points are two image points of the intersection point of the apparent contour line in the plane of the camera;
step 1.4, corresponding the two image points in step 1.3 to the plane of the projector through the absolute phase values thereof to obtain two intersection points iP1,iP2Is located atLine i ═ iP1×iP2Coordinate e of pole in the plane of the projectorrAnd projection curve C of sphere calibration object under projectorPSatisfy l ═ CP·erAnd i isP1,iP2Is located at CPFrom the above, the projection curve C of the sphere calibration object under the projector is obtainedP。
3. The calibration method of multi-camera-projector system based on sphere calibration object as claimed in claim 1, wherein the intrinsic parameters K of the camera/projector in step 2 are:
wherein f isu,fvFocal length in the u and v axis directions, s is the offset between the u and v axes, respectively, (u0,v0) Is the phase plane principal point coordinate.
4. The calibration method of multi-camera-projector system based on sphere calibration object as claimed in claim 1, wherein the bi-tangential, semi-orthogonal planning or orthogonal constraint method is applied in step 2 to obtain the intrinsic parameters of each camera and projector.
5. The calibration method of a multi-camera-projector system based on sphere calibration object as claimed in claim 1, wherein the value of α in step 3 is represented by the formula KTThe characteristic value of CK is uniquely determined, and C is a camera projection curve.
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| CN114241059B (en) * | 2021-12-17 | 2024-04-05 | 东南大学 | Synchronous calibration method for camera and light source in photometric stereo vision system |
| CN117351526A (en) * | 2023-12-05 | 2024-01-05 | 深圳纯和医药有限公司 | Intravascular ultrasound image automatic identification method for intima |
| CN117351526B (en) * | 2023-12-05 | 2024-03-22 | 深圳纯和医药有限公司 | Intravascular ultrasound image automatic identification method for intima |
| CN118505500A (en) * | 2024-07-19 | 2024-08-16 | 柏意慧心(杭州)网络科技有限公司 | Point cloud data splicing method, point cloud data splicing device, medium and electronic equipment |
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