CN110849268B - Quick phase-height mapping calibration method - Google Patents

Quick phase-height mapping calibration method Download PDF

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CN110849268B
CN110849268B CN201911255474.XA CN201911255474A CN110849268B CN 110849268 B CN110849268 B CN 110849268B CN 201911255474 A CN201911255474 A CN 201911255474A CN 110849268 B CN110849268 B CN 110849268B
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伏燕军
蔡晓奇
刘彦昭
陈建斌
钟可君
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Nanchang Hangkong University
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Abstract

The invention discloses a quick phase-height mapping calibration method, which comprises the following steps: establishing a three-dimensional measurement system; detecting the difference value of pixel coordinate values of specific points of the checkerboard shot by a camera by using a Harris angular point detection algorithm to adjust the optical axis of the CCD camera to be vertical to a reference plane; respectively obtaining absolute phase values of the high-precision standard planes before and after rotation by a time phase expansion method based on period correction; performing two-dimensional identification on the mark points on the rotated standard plane by using a centroid method to obtain pixel coordinates, and searching corresponding mark point absolute phase values in corresponding standard plane absolute phase value data; and fitting a plurality of virtual planes by using the slope of the standard plane before rotation and the absolute phase value of the mark point, and optimizing and solving system parameters by using a least square method to complete phase-height calibration. The invention greatly improves the calibration speed of the three-dimensional measurement system and has potential application prospect and practical value in the field of desktop three-dimensional scanners.

Description

Quick phase-height mapping calibration method
Technical Field
The invention relates to an optical three-dimensional measurement method, and belongs to the technical field of photoelectric detection. In particular to a fast phase-height mapping calibration method.
Background
The structured light three-dimensional imaging technology has the advantages of high precision, high speed, non-contact measurement and the like, and is widely applied to the fields of industrial detection, quality control, 3D printing, cultural relic protection and the like. Along with the industrial upgrading of the production structure in China, the requirement on the three-dimensional measurement precision of a large structural part is gradually increased, and the product quality is ensured by the quick three-dimensional precision measurement which cannot be carried out in the processing and manufacturing, process equipment and product detection links of aerospace, large ships, automobile bodies, rail transit and the like.
In phase profilometry, a conventional phase-height mapping calibration method generally uses a displacement table to drive a standard plane to move longitudinally within the depth of field range of a camera, each translation position represents a different calibration plane, and system calibration is performed according to the position of the calibration plane and the phase distribution. However, in the actual large-field measurement, moving the standard plane by the displacement table for multiple times is time-consuming and generates more accumulated errors in the process of moving the standard plane. Meanwhile, the panoramic three-dimensional measurement of a measured object can be completed by utilizing the parameter calibration of the rotating platform to realize multi-view point cloud splicing, but the problems of time-consuming calibration process, difficulty in carrying equipment, error accumulation and the like exist when the measurement system is calibrated by adopting a traditional calibration method of a displacement platform and a standard plane. Therefore, the research of a fast and high-precision calibration method is also a key problem to be solved in the field of three-dimensional measurement. The invention provides a fast phase-height mapping calibration method by fully considering the problems. The method can greatly improve the calibration speed of the three-dimensional measurement system and has potential application prospect and practical value in the field of desktop three-dimensional scanners.
Disclosure of Invention
In order to obtain the three-dimensional height information of the measured object, the invention provides a quick phase-height mapping calibration method based on a high-precision electric turntable. The specific technical scheme is as follows: a fast phase-height mapping calibration method comprises the following steps:
(1) establishing a three-dimensional measurement system: the system comprises a DLP projector, a CCD camera and a reference plane; the DLP projector and the CCD camera are at the same height, the distance between the DLP projector and the CCD camera is d, and the distance between the DLP projector and the CCD camera and the reference plane is L;
(2) detecting the difference value of pixel coordinate values of specific points of the checkerboard shot by a camera by using a Harris angular point detection algorithm to adjust the optical axis of the CCD camera to be vertical to a reference plane;
(3) respectively obtaining absolute phase values of the standard plane before and after the standard plane is driven by the high-precision electric turntable to rotate once through a time phase expansion method based on cycle correction, and finally pasting the mark points on the standard plane;
(4) performing two-dimensional identification on the mark points on the rotated standard plane by using a centroid method to obtain pixel coordinates, and searching corresponding mark point phase values in corresponding standard plane absolute phase value data according to the pixel coordinates;
(5) and fitting a plurality of virtual planes by using the slope of the standard plane before rotation and the absolute phase value of the mark point, and optimizing and solving system parameters by using a least square method to complete phase-height calibration.
Preferably, the method for fitting the virtual plane in step (5) includes: firstly, the absolute phase value information of a standard plane before rotation is used for fitting a plane equation of the standard plane, and then a virtual plane which passes through the mark point and is parallel to the reference plane is fitted by adopting the slope of the fitting plane and the absolute phase value of the mark point.
The invention has the advantages that: (1) the phase-height mapping calibration method based on the high-precision electric turntable can complete system calibration only by rotating the standard plane once, so that the system calibration speed is greatly improved; (2) because the virtual plane is fitted based on the standard plane, the random error caused by moving the standard plane in the traditional method is effectively reduced, and the calibration precision is effectively improved; (3) the invention can effectively solve the system calibration problem in the process of realizing the recovery of the integral three-dimensional shape of the measured object by using the parameter calibration of the rotating table without an additional displacement table.
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FIG. 1 is a schematic diagram of a three-dimensional measurement system of the present invention.
FIG. 2 is a calibration chart of perpendicularity of camera according to the present invention
Fig. 3 is a structural view of the electric turntable of the present invention.
FIG. 4 is a plot of the pixel coordinates of a marker point of the present invention.
Fig. 5 is a schematic diagram of the present invention.
Detailed Description
The following description will be provided in detail with reference to the accompanying drawings, which are not intended to limit the present invention, and all similar structures and similar variations using the present invention shall fall within the scope of the present invention.
A fast phase-height mapping calibration method comprises the following steps:
(1) and establishing a three-dimensional measuring system. As shown in fig. 1, the system includes a DLP projector, a CCD camera, and a reference plane; the DLP projector and the CCD camera are at the same height, the distance between the DLP projector and the CCD camera is d, and the distance between the DLP projector and the CCD camera and the reference plane is L;
(2) and (5) calibrating the verticality. And (3) carrying out perpendicularity calibration by adopting a black and white standard checkerboard, wherein the checkerboard is square, and the checkerboard is placed in close contact with the reference plane. The CCD camera collects checkerboard images, the black and white grids form corner points, pixel coordinates of the grid corner points are detected by using a Harris detection algorithm, and pixel lengths of corresponding sides of the grids are calculated by using the pixel coordinates. Because the CCD camera has distortion, a square containing a plurality of grids in the center of the camera view field is taken for measurement, the actual length and the pixel length of the grids can be measured, and the pixel equivalent is calibrated. When AB ═ CD is satisfied, the CCD camera is perpendicular to the reference plane, if AB! The direction of the CCD camera is continuously adjusted until the condition is satisfied, generally, the calibration error does not exceed one pixel. After calibration is completed, the position of the CCD camera needs to be fixed, and the verticality calibration effect is shown in figure 2.
(3) Absolute phase values are obtained for the standard plane. The DLP projector adopts an inclined projection mode, so that the phenomenon of uneven fringe broadening projected by periodic sinusoidal fringes on a reference plane can occur, and the absolute phase value of a standard plane before and after rotation on the rotary table can be accurately measured by firstly adopting a fringe four-step phase shifting method based on fringe period correction and then adopting a time phase unfolding method based on fringe period correction.
(4) An absolute phase value at each marker point is obtained. The standard circular mark point is selected, and the pixel coordinates of the circle center of the circular mark point on the standard plane before and after the rotation of the electric turntable are detected by Hough transform algorithm, as shown in FIG. 3. Then, the corresponding marker point phase value is searched in the corresponding standard plane absolute phase value data, as shown in fig. 4.
(5) A fitted plane is obtained. If the slope of a plane and the coordinates of a point crossing the plane are known, we can obtain the equation of the plane, and also obtain data information of all points on the plane. First, a virtual plane is fitted with the standard plane absolute phase values before rotation.
The principle of plane fitting is as follows:
assume that the general expression of the fitted plane equation is:
z＝a0x+a1y+a2,(a0,a1,a2arbitrary constant) (1) for n points on the standard plane before rotation: pi(xi,yi,zi) I is 0,1, …, n-1, and the above plane equation is calculated using the n-point fit such that:
Figure GDA0003074756430000031
and minimum.
To minimize S, one should satisfy:
Figure GDA0003074756430000032
namely:
Figure GDA0003074756430000033
comprises the following steps:
Figure GDA0003074756430000034
solving the linear equation set to obtain: a is0,a1,a2The slope of the standard plane before rotation, z ═ a0x+a1y+a2An expression of the plane equation is fitted before rotation. Then, the slope and the absolute phase values at the mark points obtained in the previous step are used for fitting a plurality of virtual planes parallel to the standard plane, and the planes can replace the standard plane driven by the control of a mechanical moving device in the traditional method.
(6) Phase-height calibration, also known as system geometry calibration. The essence is to calibrate the distance L between the CCD camera and the reference plane, and the distance d between the projector and the CCD camera. The corresponding relation between the phase difference of the measured object and the height thereof is as shown in formula (3)
Figure GDA0003074756430000042
Where f is a system parameter.
L, d calibration is accomplished by rotating the standard plane on a high precision electric turntable according to the phase-height formula. The high-precision electric turntable only needs to rotate once, a plurality of groups of experimental data are recorded by utilizing the phase difference between the fitted virtual plane and the standard plane before rotation, a calibration equation with L, d as an unknown number is established, and L, d calibration can be completed by theoretically two groups of experimental data. In order to improve the calibration accuracy, generally 5 marker points are selected, the relevant virtual plane is fitted, and the system geometric parameters L, d are solved by using the least square method, and the calibration process is shown in fig. 5. The derivation process of the system geometric parameter calibration is as follows:
the deformation formula for the phase-height relationship is:
Figure GDA0003074756430000043
order to
Figure GDA0003074756430000044
The above formula is simplified into：
Figure GDA0003074756430000045
From the deformation formula
Figure GDA0003074756430000046
And
Figure GDA0003074756430000047
linear, therefore, the amount of computation is reduced by determining the corresponding C1 and C2 values at each location.
As shown in FIG. 5, where O is the center of the turntable, θ is the angle of rotation of the reference plane about the axis, and p1、p2、…、pnFor marking points, hiAnd (i is 1,2, …, n) is the distance from the plane of the mark point to the reference plane. And the distance from the first mark point to the center of the circle is a, and the distance between the mark points is l. Derived from the geometric relationship:
hi＝asinθ+(n-1)lsinθ(i＝1,2,3,…,n) (8)
combined stand
Formula (II)
Figure GDA0003074756430000048
For the formula (9), the values of C1 and C2 are solved by using a least square optimization algorithm, and then L, d system parameters are solved, so that the phase-height calibration is completed.
The above description is only for the preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention shall fall within the protection scope of the present invention.

Claims (1)

1. A fast phase-height mapping calibration method is characterized by comprising the following steps:
(1) establishing a three-dimensional measurement system: the system comprises a DLP projector, a CCD camera and a reference plane; the DLP projector and the CCD camera are at the same height, the distance between the DLP projector and the CCD camera is d, and the distance between the DLP projector and the CCD camera and the reference plane is L;
(2) detecting the difference value of pixel coordinate values of specific points of the checkerboard shot by a camera by using a Harris angular point detection algorithm to adjust the optical axis of the CCD camera to be vertical to a reference plane;
(3) respectively obtaining absolute phase values of the standard plane before and after the standard plane is driven by the high-precision electric turntable to rotate once through a time phase expansion method based on cycle correction, and finally pasting the mark points on the standard plane;
(4) performing two-dimensional identification on the mark points on the rotated standard plane by using a centroid method to obtain pixel coordinates, and searching corresponding mark point phase values in corresponding standard plane absolute phase value data according to the pixel coordinates;
(5) fitting a plurality of virtual planes by using the slope of the standard plane before rotation and the absolute phase value of the mark point, and optimizing and solving system parameters by using a least square method to complete phase-height calibration;
firstly, fitting a virtual plane by using the absolute phase value of the standard plane before rotation;
the principle of plane fitting is as follows:
assume that the general expression of the fitted plane equation is:
z＝a0x+a1y+a2,(a0,a1,a2is an arbitrary constant) (1)
For n points on the standard plane before rotation: pi(xi,yi,zi) I is 0,1, …, n-1, and the above plane equation is calculated using the n-point fit such that:
Figure FDA0003074756420000011
minimum;
to minimize S, one should satisfy:
Figure FDA0003074756420000012
namely:
Figure FDA0003074756420000013
comprises the following steps:
Figure FDA0003074756420000014
solving the system of linear equations to obtain: a is0,a1,a2The slope of the standard plane before rotation, z ═ a0x+a1y+a2Fitting an expression of a plane equation prior to rotation; then, fitting a plurality of virtual planes parallel to the standard plane by using the slope and the absolute phase value at the mark point obtained in the previous step, wherein the planes can replace the standard plane driven by the control of a mechanical moving device in the traditional method;
(6) phase-height calibration, also known as system geometry calibration; the method is characterized in that the distance L between the CCD camera and a reference plane and the distance d between the projector and the CCD camera are calibrated; the corresponding relation between the phase difference of the measured object and the height thereof is as shown in formula (3)
Figure FDA0003074756420000022
Wherein f is a system parameter;
according to a phase-height formula, L, d calibration is completed by rotating a standard plane on a high-precision electric turntable; the high-precision electric turntable only needs to rotate once, a plurality of groups of experimental data are recorded by utilizing the phase difference between the fitted virtual plane and the standard plane before rotation, a calibration equation with L, d as an unknown number is established, and L, d calibration can be completed by theoretically two groups of experimental data; in order to improve the calibration precision, generally 5 mark points are selected, relevant virtual planes are fitted, and the geometric parameters L, d of the system are optimized and solved by using a least square method; the derivation process of the system geometric parameter calibration is as follows:
the deformation formula for the phase-height relationship is:
Figure FDA0003074756420000023
order to
Figure FDA0003074756420000024
The above formula is simplified as follows:
Figure FDA0003074756420000025
from the deformation formula
Figure FDA0003074756420000026
And
Figure FDA0003074756420000027
linear, therefore, by determining the corresponding C1 and C2 values at each location, the amount of computation is reduced; theta is the angle of rotation of the reference plane about the axis, p1、p2、…、pnFor marking points, hi(i is 1,2, …, n) is the distance from the plane of the mark point to the reference plane; the distance from the first mark point to the circle center is a, and the distance between the mark points is l; derived from the geometric relationship:
hi＝asinθ+(n-1)lsinθ(i＝1,2,3,…,n) (8)
combined stand
Formula (II)
Figure FDA0003074756420000031
For the formula (9), the values of C1 and C2 are solved by using a least square optimization algorithm, and then L, d system parameters are solved, so that the phase-height calibration is completed.
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