WO2016138758A1 - 一种远心成像的三维形貌测量系统标定方法 - Google Patents

一种远心成像的三维形貌测量系统标定方法 Download PDF

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WO2016138758A1
WO2016138758A1 PCT/CN2015/089903 CN2015089903W WO2016138758A1 WO 2016138758 A1 WO2016138758 A1 WO 2016138758A1 CN 2015089903 W CN2015089903 W CN 2015089903W WO 2016138758 A1 WO2016138758 A1 WO 2016138758A1
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telecentric
pixel
imaging device
translation stage
calibration
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French (fr)
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田劲东
李东
颜思晨
田勇
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Shenzhen University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N13/00—Stereoscopic video systems; Multi-view video systems; Details thereof
    • H04N13/20—Image signal generators
    • H04N13/204—Image signal generators using stereoscopic image cameras
    • H04N13/246—Calibration of cameras
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
    • G01B11/25—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures by projecting a pattern, e.g. one or more lines, moiré fringes on the object
    • G01B11/2504—Calibration devices
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
    • G01B11/25—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures by projecting a pattern, e.g. one or more lines, moiré fringes on the object
    • G01B11/254—Projection of a pattern, viewing through a pattern, e.g. moiré
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/50—Depth or shape recovery
    • G06T7/521—Depth or shape recovery from laser ranging, e.g. using interferometry; from the projection of structured light
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/80—Analysis of captured images to determine intrinsic or extrinsic camera parameters, i.e. camera calibration
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N13/00—Stereoscopic video systems; Multi-view video systems; Details thereof
    • H04N13/20—Image signal generators
    • H04N13/204—Image signal generators using stereoscopic image cameras
    • H04N13/207—Image signal generators using stereoscopic image cameras using a single two-dimensional [2D] image sensor
    • H04N13/236—Image signal generators using stereoscopic image cameras using a single two-dimensional [2D] image sensor using varifocal lenses or mirrors
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N13/00—Stereoscopic video systems; Multi-view video systems; Details thereof
    • H04N13/20—Image signal generators
    • H04N13/204—Image signal generators using stereoscopic image cameras
    • H04N13/254—Image signal generators using stereoscopic image cameras in combination with electromagnetic radiation sources for illuminating objects
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N13/00—Stereoscopic video systems; Multi-view video systems; Details thereof
    • H04N13/20—Image signal generators
    • H04N13/296—Synchronisation thereof; Control thereof

Definitions

  • the invention belongs to the field of three-dimensional data imaging and optical three-dimensional reconstruction, and in particular relates to a calibration method of a three-dimensional shape measurement system for telecentric imaging.
  • the three-dimensional shape measurement method based on projected sinusoidal stripe structured light is widely used due to its advantages such as simple principle, fast calculation speed and high measurement accuracy, including phase detection profilometry and Fourier transform profilometry.
  • the reference fringe pattern can be obtained by projecting a sinusoidal fringe pattern on the reference plane by the projector. When the object to be inspected is placed on the reference plane, the deformed fringe pattern can be obtained, and the two fringe patterns can obtain the 2D absolute phase difference, thereby obtaining the measured object. 3D depth information. Therefore, it is necessary to calibrate the phase-height transformation relationship of the system and the camera parameters.
  • the technical problem to be solved by the present invention is to provide a calibration method for a three-dimensional shape measurement system for telecentric imaging, which solves the problem that the calibration of the three-dimensional shape measurement system in the prior art is complicated, and some parameters are difficult to be accurately calibrated to affect the three-dimensional shape measurement system. Problems such as accuracy.
  • a calibration method for a three-dimensional shape measurement system for telecentric imaging comprising the following steps:
  • Step S1 constructing a telecentric three-dimensional topography measuring system, the measuring system comprises: a telecentric projection device, a telecentric imaging device, a translation stage; the optical axis of the telecentric imaging device is perpendicular to the horizontally placed translation stage, and the telecentric projection device The optical axis is at an angle to the translation stage, and the optical axis of the telecentric imaging device is controlled to be in the same plane as the optical axis of the telecentric projection device;
  • Step S2 making the translation stage within a common depth of field range of the telecentric projection device and the telecentric imaging device, controlling the telecentric projection device to project a sinusoidal fringe pattern on the translation stage, the telecentric imaging device collecting the sinusoidal fringe pattern, and selecting the telecentric camera Any pixel on the image plane of the device is used as a calibration pixel, and the absolute phase value of the calibration pixel is obtained by a multi-step phase shift method, and the translation stage height value at this time is recorded;
  • the control translation stage performs a plurality of displacements along the optical axis direction of the telecentric imaging device within a common depth of field of the telecentric projection device and the telecentric imaging device, and when the translation stage is moved to a different height, the pixel for calibration at the height is acquired. Absolute phase value and record the corresponding translation stage height value;
  • Step S3 Converting the pixel coordinates on the image plane of the telecentric imaging device into world coordinates by calibrating the parameters of the telecentric imaging device.
  • the present invention can also be improved as follows:
  • step S2 includes:
  • Step S21 controlling the translation stage to adjust the translation stage to be in the lowest position of the height measurement range within the common depth of field range of the telecentric projection apparatus and the telecentric imaging apparatus, and record the lowest height z 0 of the translation stage ;
  • the intensity I L ( ⁇ , ⁇ ) expression is:
  • the wrapping phase at the pixel ( ⁇ , ⁇ ) for the calibration can be found as ⁇ ( ⁇ , ⁇ ):
  • step S32 includes:
  • Step S321 establishing an orthorectic transformation model when the object image is double telecentric lens imaging without considering the lens distortion; the ortho-transformation model of the object image double telecentric lens imaging is:
  • (x ⁇ i , y ⁇ i ) is the image coordinate of a series of feature points in the imaging plane coordinate system of the telecentric imaging device
  • (X ⁇ i , Y ⁇ i , Z ⁇ i ) is a series of feature points in the world coordinate system
  • m is the magnification of the object's double telecentric lens
  • R [r ij ] is the rotation matrix
  • T [t x t y t z ]
  • T is the translation matrix
  • d ⁇ and d ⁇ are each pixel Physical dimensions in the X-axis and Y-axis directions;
  • ( ⁇ 0 , ⁇ 0 ) is the central pixel point coordinate on the image plane of the telecentric imaging device, and is also the origin of the image coordinates on the imaging plane;
  • Step S322 Considering lens distortion of the telecentric imaging apparatus, the expression of the lens distortion is:
  • Distortion parameters for each pixel in the X-axis direction For each pixel in the Y-axis direction of the distortion parameter; k 1 is the parameter of the degree of radial distortion, h 1 , h 2 is the parameter of the degree of centrifugal distortion, s 1 , s 2 is the parameter of the degree of thin prism distortion;
  • ( ⁇ 0 , ⁇ 0 ) is the central pixel point coordinate on the image plane of the telecentric imaging device, and is also the origin of the image coordinates on the imaging plane;
  • Step S323 The parameters of the telecentric imaging device include an external parameter rotation matrix R, a translation matrix T, and an initial value of the magnification parameter m of the object image double telecentric lens;
  • the world coordinates (X ⁇ i , Y ⁇ i , Z ⁇ i ) of the series of feature points and the corresponding series of pixel coordinates ( ⁇ i , ⁇ i ) are obtained according to equations (5) and (6) without considering distortion.
  • the pixel coordinates represented by the image coordinates in the equation (8) are brought into the equation (5) to obtain the initial values of the internal parameters k 1 , h 1 , h 1 , s 1 , s 2 of the telecentric imaging apparatus;
  • N is the total number of feature points
  • the outer parameters R, T and the internal parameters k 1 , h 1 , h 2 , s 1 , s 2 and the object image double telecentric lens are obtained by least squares method.
  • Step S324 according to the obtained telecentric imaging device external parameters R, T and internal parameters k 1 , h 1 , h 2 , s 1 , s 2 and the magnification factor parameter m of the object image double telecentric lens,
  • the pixel coordinates ( ⁇ , ⁇ ) on the image plane of the telecentric imaging device are converted into world coordinates (X ⁇ , Y ⁇ ).
  • the invention has the beneficial effects that the calibration method of the three-dimensional topography measuring system for telecentric imaging is that the present invention utilizes the characteristics of the telecentric lens to construct a three-dimensional appearance measuring system based on phase shift projection, in which the projection device and the imaging device both use double
  • the side telecentric lens in the depth of field of the telecentric projection system, causes the projection device to project a sinusoidal fringe pattern with a constant period on the reference plane, and establishes the image plane of the telecentric camera device within the depth of field of the telecentric camera device.
  • the linear relationship between the absolute phase value of one pixel and the height of the translation stage can determine the linear relationship between the phase and the height of the three-dimensional topography measurement system; the phase and the height are full in the present invention.
  • the linear relationship of the foot only needs to measure the linear relationship between the absolute phase value of one pixel and the height of the translation stage. The solution calculation is small, the accuracy is high, the operability is strong, and the practicability is strong.
  • the three-dimensional shape measurement system of the telecentric imaging of the present invention removes many restrictions on the position of the device in the conventional three-dimensional shape measurement system, such as: (1) does not require the optical axis P 1 P 2 of the projector and the camera The optical axis C 1 C 2 of the device is strictly intersected on the reference plane.
  • the imaging device can capture the panoramic view of the measured object; (2) In the telecentric system, the exit of the projector and the entrance of the imaging device are located at infinity, so there is no requirement that the entrance of the projector and the exit of the imaging device be planed to the reference plane; (3) the system There is also no positional restriction on the principal point P 2 of the image telecentric lens in the projector and the principal point C 2 of the object telecentric lens in the imaging apparatus as long as the translation stage is within the respective depth of field.
  • the ortho-injection model of the object image double telecentric lens is established, and only the inner and outer parameters of the telecentric camera device need to be calibrated to a height within the depth of field range. All the heights in the depth of field of the telecentric system are used to correspond to this relationship, which simplifies the calibration process.
  • the optimization method is used to correct the parameters and improve the accuracy of the system.
  • FIG. 1 is a schematic flow chart of a calibration method of a three-dimensional topography measuring system according to the present invention
  • FIG. 2 is a schematic view showing the position of a device for a calibration method of a telecentric three-dimensional topography measuring system according to the present invention
  • step S2 of the present invention is a schematic flow chart of a specific embodiment of step S2 of the present invention.
  • step S2 of the present invention is a linear fitting curve diagram of an absolute phase value and a translation stage height value in a specific embodiment of step S2 of the present invention
  • step S3 of the present invention is a schematic flow chart of a specific embodiment of step S3 of the present invention.
  • FIG. 7 is a schematic flowchart of a specific embodiment of step S32 of the present invention.
  • FIG. 8 is a schematic diagram of an imaging model of an imaging apparatus having a telecentric lens.
  • Telecentric projection device 102
  • telecentric imaging device 103
  • translation stage 104
  • the invention provides a calibration method for a three-dimensional shape measurement system, and builds a three-dimensional topography measurement system for telecentric imaging, so that when the translation stage moves within the depth of field of the telecentric projection device, the telecentric projection device projects onto the translation stage.
  • the sinusoidal fringe pattern with a constant period is used to establish a linear relationship between the absolute phase value of any pixel on the image plane of the imaging device and the height of the translation stage in the depth of field of the telecentric imaging device, thereby determining the three-dimensional shape.
  • the phase--height mapping relationship of the measurement system at the same time, the method establishes the orthorectal transformation model of the object-like double telecentric lens, and only needs to calibrate the internal and external parameters of the telecentric camera device for a height within the depth of field range. All heights within the depth of field of the heart system use this relationship to simplify the calibration process.
  • FIG. 1 is a schematic flow chart of a calibration method of a three-dimensional topography measuring system according to the present invention
  • FIG. 2 is a schematic diagram of a device position of a calibration method for a telecentric three-dimensional topography measuring system according to the present invention, as shown in FIG.
  • the calibration method of the invention comprises the following steps:
  • Step S1 Building a telecentric three-dimensional topography measuring system, the measuring system comprising: a telecentric projection device 101, a telecentric imaging device 102, a translation stage 103; the optical axis of the telecentric imaging device 102 is perpendicular to the horizontally placed translation stage 103 The optical axis of the telecentric projection device 101 is at an angle to the translation stage 103, and controls the optical axis of the telecentric imaging apparatus 101 to be in the same plane as the optical axis of the telecentric projection apparatus 102.
  • the telecentric projection device 101 can be a digital projector using a dual telecentric lens
  • the digital projector can be a digital liquid crystal projection device (LCD projector), a digital micromirror projection device (DMD projector) or a silicon substrate.
  • LCD projector digital liquid crystal projection device
  • DMD projector digital micromirror projection device
  • silicon substrate a silicon substrate.
  • Liquid crystal projector (LCOS projector) a computer image processing system can be used to conveniently generate a grayscale stripe pattern and written into a digital projection device
  • the telecentric camera device 102 can be a camera that uses an object like a double telecentric lens, and the camera can be charge coupled.
  • the translation stage 103 when the measurement system is used to measure three-dimensional information of an object, the object to be tested 104 is placed on the translation stage 103, the translation stage 103 is horizontally placed and can move up and down; 103 can be an electronically controlled translation stage, an electric stepper device that controls the stepping distance by a computer; the translation stage 103 can also be a translation stage that manually controls the movement.
  • FIG. 2 is a schematic diagram of a device position of a calibration method of a telecentric three-dimensional topography measuring system according to the present invention.
  • the relative positions of the telecentric projection device 101 and the telecentric imaging device 102 are adjusted to make the translation stage 103 far away.
  • the structural depth of light within the common depth of field of the cardiac projection device 101 and the telecentric imaging device 102 and ensuring that the telecentric projection device 101 projects onto the translation stage 103 can be captured by the telecentric imaging device 102.
  • the object image double telecentric lens of the telecentric projection apparatus 101 of FIG. 2 respectively uses its principal points P 1 , P 2 to indicate the projected light, and also the object image double telecentric lens of the telecentric imaging apparatus 102 respectively.
  • the main points C 1 , C 2 are used to illustrate the imaging of light.
  • Step S2 The translation stage 103 is placed within a common depth of field range of the telecentric projection apparatus 101 and the telecentric imaging apparatus 102, the telecentric projection apparatus 101 is controlled to project a sinusoidal fringe pattern to the translation stage 103, and the telecentric imaging apparatus 102 acquires a sinusoidal fringe pattern. Selecting any pixel on the image plane of the telecentric imaging device 102 as the calibration pixel, using the multi-step phase shift method to obtain the absolute phase value of the calibration pixel, and recording the height value of the translation stage 103 at this time;
  • the control translation stage 103 performs a plurality of displacements along the optical axis direction of the telecentric imaging apparatus 102 within a common depth of field of the telecentric projection apparatus 101 and the telecentric imaging apparatus 102, and acquires the height when the translation stage 103 is moved to a different height. Calibrating the absolute phase value of the pixel, and recording the corresponding translation stage 103 height value;
  • FIG. 3 is a schematic flowchart of a specific embodiment of step S2 of the present invention. As shown in FIG. 3, in the embodiment, the step S2 includes:
  • Step S21 Control the translation stage 103 to adjust the translation stage 103 to be at the lowest position of the height measurement range, and record the lowest height of the translation stage 103, within the common depth of field range of the telecentric projection apparatus 101 and the telecentric imaging apparatus 102. 0 ;
  • Step S22 Using the computer to write a sinusoidal fringe pattern with a period T 0 to implant the telecentric projection device 101, so that the telecentric projection device 101 projects four sinusoidal fringes with a constant period to the translation stage 103; the four sinusoidal fringes are first sinusoidal.
  • the pixel coordinates of the calibration pixel in the image coordinate system of the telecentric imaging apparatus 102 are ( ⁇ , ⁇ ), and the pixel is imaged at the point (x, y) on the translation stage.
  • the pixel on the image plane of the device, the projection device 101 and the imaging device 102 both use the bilateral telecentric lens in the three-dimensional topography measurement system of the telecentric imaging matched with the method of the present invention, and the depth of field in the telecentric projection system In the range, the projection device projects onto the reference plane as a periodic sinusoidal fringe pattern, so that the absolute phase value at the point (x, y) on the translation stage is equal to the absolute phase value at the pixel point ( ⁇ , ⁇ ), and calibrated with intensity I L of the pixel ( , ⁇ ) expression is:
  • the parcel phase at the pixel ( ⁇ , ⁇ ) for calibration can be obtained as ⁇ ( ⁇ , ⁇ ):
  • FIG. 4 is a schematic structural diagram of controlling the translation stage to move in the system in step S23.
  • the control translation stage 103 is photographed along the telecentric range within the common depth of field of the telecentric projection apparatus 101 and the telecentric imaging apparatus 102.
  • M is a linear scale factor. Since the phase difference that is highly modulated by the object is often obtained in the three-dimensional topography measurement, it is only necessary to pay attention to the accuracy of the linear scale factor in the linear relationship.
  • the telecentric lens has a characteristic that the image magnification of the image does not change with the change of the object distance within a certain object distance range. Therefore, in the three-dimensional shape measurement system of the telecentric imaging of the present invention, only the depth of field is required. In the range calibration, the linear relationship between the absolute phase value and the height at the pixel point can be used to map any pixel on the image of the telecentric camera device, which simplifies the calibration process.
  • step S2 of the present invention To clarify the absolute phase value in the three-dimensional topography measurement system for telecentric imaging of step S2 of the present invention
  • the process of the conversion relationship with the height z is further described below with reference to the specific embodiment of the present embodiment.
  • the telecentric imaging device in this embodiment adopts Daheng industrial grade CMOS camera DH-HV1351-UC, the pixel is 1280 ⁇ 1024, the lens is Daheng's object double telecentric lens GC0230105; the telecentric projection device adopts HP's
  • the projector AX325AA has a resolution of 800 ⁇ 600, and the lens is a large constant image double telecentric lens GC0230106;
  • the translation stage is a translation stage that manually controls the up and down movement, and its movement accuracy is 0.01 mm.
  • the position of the projector and the camera is as shown in FIG. 2 and maintained at a certain angle, and the translation stage is controlled to translate in the vertical direction along the z-axis.
  • the phase shift of the first sinusoidal fringe is defined as 0, and the four sinusoidal fringes captured by the camera in sequence can be expressed as:
  • the four sinusoidal fringe patterns of the equal phase difference are projected for the translation stage at each height, and the camera sequentially acquires the four sinusoidal fringe patterns, which can be obtained by the four-step phase shift method.
  • a pixel point with an index of (710, 571) on the image plane of the camera is selected, and the distance of the translation stage is manually moved upward by 0.05 mm, and the minimum height that can be achieved by the translation stage is 0 mm, and the calibration height range is 2.40 mm. To 2.70mm.
  • the absolute phase value of the pixel with index (710, 571) on the camera image plane is solved by the four-step phase shift method.
  • the correspondence with the translation stage height z is as shown in the following table:
  • FIG. 5 is a linear fitting curve of the absolute phase value and the translation stage height value in a specific implementation of the step S2 of the present invention. It is worth noting that this case is to avoid the phase unwrapping operation, and the height is calibrated from 2.40mm to 2.70mm. In fact, the height measurement range of the telecentric imaging measurement system built in this case is as high as 5 mm.
  • the present invention further includes a step S3 of converting the pixel coordinates on the image plane of the telecentric imaging device into world coordinates by calibrating the parameters of the telecentric imaging device.
  • FIG. 6 is a schematic flowchart of a specific embodiment of step S3 of the present invention. As shown in FIG. 6 , in step S3 in this embodiment, the method specifically includes:
  • Step S31 adjusting the translation stage to a common depth of field range of the telecentric projection device and the telecentric imaging device, placing the calibration on the translation stage, projecting white light from the telecentric projection device to the calibration frame, and collecting the calibration image by the telecentric imaging device. Extracting feature points from the acquired images to obtain a series of world coordinates (X ⁇ i , Y ⁇ i , Z ⁇ i ) of feature points in world coordinates, and a series of corresponding points on the image coordinate system of the telecentric imaging device Pixel coordinates ( ⁇ i , ⁇ i );
  • Step S32 using the correspondence between the world coordinates (X ⁇ i , Y ⁇ i , Z ⁇ i ) of a series of feature points and the pixel coordinates ( ⁇ i , ⁇ i ), calibrating the parameters of the telecentric imaging device, and the image plane of the telecentric imaging device
  • the upper pixel coordinates ( ⁇ , ⁇ ) are converted to world coordinates (X ⁇ , Y ⁇ ).
  • FIG. 7 is a schematic flowchart of a specific embodiment of step S32 of the present invention. As shown in FIG. 7, the step S32 includes:
  • Step S321 establishing an orthorectic transformation model when the object image is double telecentric lens imaging without considering the lens distortion; the ortho-transformation model of the object image double telecentric lens imaging is:
  • (x ⁇ i , y ⁇ i ) is the image coordinate of a series of feature points in the imaging plane coordinate system of the telecentric imaging device
  • (X ⁇ i , Y ⁇ i , Z ⁇ i ) is a series of feature points in the world coordinate system
  • m is the magnification of the object's double telecentric lens
  • R [r ij ] is the rotation matrix
  • T [t x t y t z ]
  • T is the translation matrix
  • d ⁇ and d ⁇ are each pixel Physical dimensions in the X-axis and Y-axis directions;
  • ( ⁇ 0 , ⁇ 0 ) is the central pixel point coordinate on the image plane of the telecentric imaging device, and is also the origin of the image coordinates on the imaging plane.
  • FIG. 8 is a schematic diagram of an imaging model of an imaging apparatus having a telecentric lens.
  • the imaging model of the telecentric imaging apparatus in this embodiment is as shown in FIG. 8.
  • the coordinates of the feature point P in the world coordinate system are (X ⁇ , Y ⁇ , Z). ⁇ ), p(X c , Y c , Z c ) is the coordinate of the feature point P in the telecentric camera coordinate system; if it is an ideal orthographic model, then P(X c , Y c , Z c )
  • the ideal image coordinate in the imaging plane coordinate system is p(x u , y u ).
  • the telecentric lens performs zooming orthographic projection.
  • the conversion relationship between the image coordinates of the imaging plane and the coordinates of the telecentric camera device is expressed as follows: Without considering the lens distortion, the ideal (non-distortion) of the projection point P of any projection point P is expressed as:
  • m is the effective magnification of the telecentric lens.
  • the imaging plane coordinate system xoy is consistent with the image plane coordinate system of the telecentric camera, and therefore, the expression from the imaging plane coordinates (x u , y u ) to the pixel coordinates (u, v) is expressed.
  • the formula is:
  • du and dv are the physical dimensions of a pixel in the x and y directions, respectively, ( ⁇ 0 , ⁇ 0 ) is the central pixel point coordinate on the image plane of the telecentric imaging device, and is also the origin of the image coordinates on the imaging plane.
  • Equation (5-d) is the orthorectmic transformation model when the object image is double telecentric lens.
  • Step S322 Considering lens distortion of the telecentric imaging apparatus, there are mainly three types of lens distortion: radial distortion, eccentric distortion, and thin prism distortion; in this embodiment, effective distortion is considered, and the expression of lens distortion is:
  • Distortion parameters for each pixel in the X-axis direction For each pixel in the Y-axis direction of the distortion parameter; k 1 is the parameter of the degree of radial distortion, h 1 , h 2 is the parameter of the degree of centrifugal distortion, s 1 , s 2 is the parameter of the degree of thin prism distortion;
  • ( ⁇ 0 , ⁇ 0 ) is the central pixel point coordinate on the image plane of the telecentric imaging device, and is also the origin of the image coordinates on the imaging plane.
  • Step S323 The parameters of the telecentric imaging device include an external parameter rotation matrix R, a translation matrix T, and an initial value of the magnification parameter m of the object image double telecentric lens;
  • the world coordinates (X ⁇ i , Y ⁇ i , Z ⁇ i ) of the series of feature points and the corresponding series of pixel coordinates ( ⁇ i , ⁇ i ) are obtained according to equations (5) and (6) without considering distortion.
  • the pixel coordinates represented by the image coordinates in the equation (8) are brought into the equation (5) to obtain the initial values of the internal parameters k 1 , h 1 , h 1 , s 1 , s 2 of the telecentric imaging apparatus;
  • N is the total number of feature points, and the outer parameters of the telecentric imaging device m, R, T and the internal parameters k 1 , h 1 , h 2 , s 1 , s 2 are accurately obtained by least squares method;
  • Step S324 according to the obtained telecentric imaging device external parameters R, T and internal parameters k 1 , h 1 , h 2 , s 1 , s 2 and the magnification factor parameter m of the object image double telecentric lens,
  • the pixel coordinates ( ⁇ , ⁇ ) on the image plane of the telecentric imaging device are converted into world coordinates (X ⁇ , Y ⁇ ).

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Abstract

一种远心成像的三维形貌测量系统标定方法，包括：步骤S1:搭建远心三维形貌测量系统；S2：控制远心投影设备对平移台投射正弦条纹图，远心摄像设备采集所述正弦条纹图；多次移动平移台，利用多步相移法得到远心摄像设备图像平面上标定用像素点处的绝对相位值，将标定用像素点处的绝对相位值与高度值进行线性拟合，得到测量系统的相位--高度转换关系式；S3：通过标定远心摄像设备的参量，将远心摄像设备图像平面上的像素坐标转换为世界坐标。该方法中相位与高度满足线性关系，只需测得一个像素点的绝对相位值与平移台高度的线性关系，求解运算量小，精确度高，可操作性强，实用性强；另外，该方法还提供了一种物像双远心镜头的正射变换模型，简化了标定过程。

Description

一种远心成像的三维形貌测量系统标定方法 技术领域
本发明属于三维数据成像和光学三维重建领域，具体涉及一种远心成像的三维形貌测量系统标定方法。
背景技术
在三维形貌测量系统中，基于投影正弦条纹结构光的三维形貌测量方法由于原理简单、计算速度快、测量精度高等优点而被大量使用，包括相位检测轮廓术和傅里叶变换轮廓术等。通过投影仪对参考平面投射正弦条纹图可得到参考条纹图，当在参考平面上放置被检物体时可得到变形条纹图，由两幅条纹图可得到2D绝对相位差，进而得到被测物体的3D深度信息。因此需要对系统的相位--高度转化关系以及摄像机参数进行标定。但在传统的单目三维形貌测量系统中，由于投影仪与摄像机使用普通镜头所存在的非线性，投影仪投射到参考平面上的不再是周期恒定的正弦条纹图，因此有人提出使用软件编程在投影仪数字微镜上产生不均匀正弦条纹，从而在系统可测量范围内投影生成空间上周期恒定分布的条纹图。也有人提出使用离焦的反复使二值结构条纹图生成理想的正弦条纹图。这些方法均需要复杂的系统标定过程，并且有些参量很难精确标定，如摄像机镜头的光心到参考平面的距离、投影仪与摄像机光轴的夹角等，而标定的精确性决定了任何一种三维形貌测量系统的精度。
发明内容
本发明所要解决的技术问题是提供一种远心成像的三维形貌测量系统标定方法，解决现有技术中三维形貌测量系统标定复杂、部分参量很难精确标定从而影响三维形貌测量系统的精度等问题。
本发明解决上述技术问题的技术方案如下：
一种远心成像的三维形貌测量系统标定方法，所述标定方法包括如下步骤：
步骤S1:搭建远心三维形貌测量系统，所述测量系统包括：远心投影设备、远心摄像设备、平移台；远心摄像设备的光轴垂直于水平放置的平移台，远心投影设备的光轴与平移台成一夹角，并控制远心摄像设备的光轴与远心投影设备的光轴处于同一平面内；
步骤S2：使平移台处于远心投影设备和远心摄像设备的共同景深范围内，控制远心投影设备对平移台投射正弦条纹图，远心摄像设备采集所述正弦条纹图，选取远心摄像设备图像平面上的任一像素点作为标定用像素点，利用多步相移法解得该标定用像素点的绝对相位值，并记录此时的平移台高度值；
控制平移台在远心投影设备和远心摄像设备的共同景深范围内沿远心摄像设备的光轴方向进行数次位移，在移动平移台至不同高度时，获取此高度下标定用像素点的绝对相位值，并记录相应的平移台高度值；
对获得的平移台的高度值与相应的标定用像素点的绝对相位值进行线性拟合，建立远心成像的三维形貌测量系统中绝对相位值与平移台高度值的转换关系；
步骤S3：通过标定远心摄像设备的参量，将远心摄像设备图像平面上的像素坐标转换为世界坐标。
在上述技术方案的基础上，本发明还可以做如下改进：
进一步，所述步骤S2，其具体包括：
步骤S21：控制所述平移台在所述远心投影设备和远心摄像设备的共同景深范围内，调整所述平移台使它处于高度测量范围的最低位置，记下平移台的最低高度z0；
步骤S22：利用计算机编写周期为T0的正弦条纹图植入所述远心投影设备，使所述远心投影设备向所述平移台投射周期恒定的四幅正弦条纹图；所述四幅正弦条纹图以第一幅正弦条纹图为基础分别进行了2πL/4(L＝0,1,2,3)的相移；所述远心摄像设备按顺序采集四幅条纹图；选取所述远心摄像设备图像平面上的任一像素点作为标定用像素点，设所述标定用像素点在所述远心摄像设备的图像坐标系中的像素坐标为(μ,ν)；所述标定用像素点的光强IL(μ,ν)表达式为：
Figure PCTCN2015089903-appb-000001
其中L＝0,1,2,3，a(μ,ν)为背景光强，b(μ,ν)为条纹对比度，
Figure PCTCN2015089903-appb-000002
为标定用像素点(μ,ν)处的绝对相位值；
按照四步相移法，可求得所述标定用像素点(μ,ν)处的包裹相位为φ(μ,ν)：
Figure PCTCN2015089903-appb-000003
由于包裹相位的值域被切断在[-π,π]之间，须将其进行相位展开，得到所述标定用像素点(μ,ν)处绝对相位值
Figure PCTCN2015089903-appb-000004
为：
Figure PCTCN2015089903-appb-000005
其中k(μ,ν)＝±1；
步骤S23：控制所述平移台在所述远心投影设备和远心摄像设备的共同景深范围内沿所述远心摄像设备的光轴方向等间距移动△z的距离，使所述平移台处于zj＝z0+j△z(j＝0，1，2，……，n)的不同高度处，按照所述步骤S22的方法分别求得当平移台处于zj(j＝0,1,2,……,n)的高度时标定用像素点(μ,ν)处绝对相位值
Figure PCTCN2015089903-appb-000006
步骤S24：对获得的平移台的不同高度zj(j＝0,1,2,……,n)与相应的标定用像素点(μ,ν)的绝对相位值
Figure PCTCN2015089903-appb-000007
进行线性拟合；得到远心成像的三维形貌测量系统中绝对相位值与高度的线性转换关系式：
Figure PCTCN2015089903-appb-000008
其中M为线性比例因子。
进一步，所述步骤S32，其具体包括：
步骤S321：在不考虑镜头畸变情况下，建立物像双远心镜头成像时的正射变换模型；所述物像双远心镜头成像时的正射变换模型为：
Figure PCTCN2015089903-appb-000009
其中，(xμi,yμi)为一系列特征点在所述远心摄像设备的成像平面坐标系中的图像坐标，(Xωi,Yωi,Zωi)为一系列特征点在世界坐标系中的世界坐标，m为物像双远心镜头的放大倍数，R＝[rij]为旋转矩阵，T＝[tx ty tz]T为平移矩阵，dμ和dν分别为每个像素在X轴、Y轴方向上的物理尺寸；
在不考虑镜头畸变情况下，所述远心摄像设备图像平面上的像素坐标与远心摄像设备成像平面上的图像坐标的对应关系为：
Figure PCTCN2015089903-appb-000010
其中(μ0,ν0)为远心摄像设备图像平面上的中心像素点坐标，也是成像平面上图像坐标的原点；
步骤S322：考虑所述远心摄像设备的镜头畸变，所述镜头畸变的表达式为：
Figure PCTCN2015089903-appb-000011
其中，
Figure PCTCN2015089903-appb-000012
为每个像素在X轴方向上的畸变参数，
Figure PCTCN2015089903-appb-000013
为每个像素在Y轴方向上的畸变参数；k1为径向畸变程度的参数，h1、h2为离心畸变程度的参数，s1、s2为薄棱镜畸变程度的参数；
建立所述远心摄像设备图像平面上的像素坐标(μi,νi)与远心摄像设备成像平面上的图像坐标(xμi,yμi)的对应关系：
Figure PCTCN2015089903-appb-000014
其中(μ0,ν0)为远心摄像设备图像平面上的中心像素点坐标，也是成像平面上图像坐标的原点；
步骤S323：所述远心摄像设备的参量包括外参数旋转矩阵R、平移矩阵T以及物像双远心镜头的放大倍数参数m的初值；
由所述一系列特征点的世界坐标(Xωi,Yωi,Zωi)和对应的一系列像素坐标(μi,νi)根据式(5)、(6)求在不考虑畸变的情况下远心摄像设备的外参数R、T以及物像双远心镜头的放大倍数参数m的初值；
再将式(8)中用图像坐标表示的像素坐标带入式(5)中求远心摄像设备的内参数k1、h1、h1、s1、s2的初值；
由远心摄像设备的内外参数初值、物像双远心镜头的放大倍数参数m的初值和特征点的像素坐标(μi,νi)，反求得到考虑了镜头畸变的一系列特征点的世界坐标
Figure PCTCN2015089903-appb-000015
建立目标函数：
Figure PCTCN2015089903-appb-000016
其中，N为特征点总数，通过最小二乘法求得所述远心摄像设备外参数R、T和内参数k1、h1、h2、s1、s2以及物像双远心镜头的放大倍数参数m的精确值；
步骤S324：根据得到的所述远心摄像设备外参数R、T和内参数k1、h1、h2、s1、s2以及物像双远心镜头的放大倍数参数m，将所述远心摄像设备图像平面上的像素坐标(μ,ν)转换为世界坐标(Xω,Yω)。
本发明一种远心成像的三维形貌测量系统标定方法的有益效果在于：本发明利用远心镜头的特性搭建基于相移投影的三维相貌测量系统，该系统中投影设备与摄像设备均使用双侧远心镜头，在远心投影系统的景深范围内，使得投影设备投射到参考平面上的为周期恒定的正弦条纹图，在远心摄像设备的景深范围内，建立远心摄像设备图像平面上任一像素点的绝对相位值与平移台高度一一对应的线性关系，便可以确定该三维形貌测量系统的相位与高度一一对应的线性关系；本发明中相位与高度满 足线性关系，只需测得一个像素点的绝对相位值与平移台高度的线性关系，求解运算量小，精确度高，可操作性强，实用性强。
同时，本发明远心成像的三维形貌测量系统解除了传统的三维形貌测量系统中对设备摆放位置的许多限制，如：(1)不要求投影仪的光轴P1P2与摄像设备的光轴C1C2严格交于参考平面上一点，只要光轴P1P2与光轴C1C2共面，摄像设备能捕捉到被测物体的全景即可；(2)由于远心系统中投影仪的出瞳与摄像设备的入瞳都位于无穷远处，因此没有投影仪的入瞳与摄像设备的出瞳的连线须平面于参考平面的要求；(3)此系统也没有对投影仪中像方远心镜头的主点P2与摄像设备中物方远心镜头的主点C2作出任何位置上的约束，只要平移台在各自的景深范围内即可。
另外，本发明在求解远心摄像设备的内外参数过程中，建立了物像双远心镜头的正射变换模型，只需要对景深范围内的一个高度标定远心摄像设备的内外参数，便可以将远心系统景深范围内的所有高度都运用这种关系去对应，简化了标定过程，同时在参数标定过程中，采用求解最优化的方法修正参数，提高系统的精度。
附图说明
图1为本发明一种三维形貌测量系统的标定方法的流程示意图；
图2为本发明一种远心三维形貌测量系统的标定方法的设备位置示意图；
图3为本发明步骤S2的一具体实施例的流程示意图；
图4为步骤S23中控制平移台在系统中移动的结构示意图，
图5为本发明步骤S2一具体实施例中绝对相位值与平移台高度值的线性拟合曲线图；
图6为本发明步骤S3的一具体实施例的流程示意图；
图7为本发明步骤S32的一具体实施例的流程示意图；
图8为具有远心透镜的摄像设备的成像模型示意图。
附图中，各标号所代表的部件列表如下：
101、远心投影设备，102、远心摄像设备，103、平移台，104、待测物体。
具体实施方式
以下结合附图对本发明的原理和特征进行描述，所举实例只用于解释本发明，并非用于限定本发明的范围。
本发明一种三维形貌测量系统的标定方法，搭建了一套远心成像的三维形貌测量系统，使得平移台在远心投影设备的景深范围内移动时，远心投影设备投射到平移台上的为周期恒定的正弦条纹图，在远心摄像设备的景深范围内，建立摄像设备图像平面上任一像素点的绝对相位值与平移台高度一一对应的线性关系，便可以确定该三维形貌测量系统的相位--高度映射关系；同时本方法建立了物像双远心镜头的正射变换模型，只需要对景深范围内的一个高度标定远心摄像设备的内外参数，便可以将远心系统景深范围内的所有高度都运用这种关系去对应，简化了标定过程。
图1为本发明一种三维形貌测量系统的标定方法的流程示意图，图2为本发明一种远心三维形貌测量系统的标定方法的设备位置示意图，如图1、2所示，本发明所述标定方法包括如下步骤：
步骤S1:搭建远心三维形貌测量系统，所述测量系统包括：远心投影设备101、远心摄像设备102、平移台103；远心摄像设备102的光轴垂直于水平放置的平移台103，远心投影设备101的光轴与平移台103成一夹角，并控制远心摄像设备101的光轴与远心投影设备102的光轴处于同一平面内。
其中，远心投影设备101可以为使用物像双远心镜头的数字投影仪，数字投影仪可以是数字液晶投影装置(LCD投影仪)、数字微镜投影装置(DMD投影仪)或硅基片液晶投影装置(LCOS投影仪)，可用计算机图像处理系统方便地生成灰度条纹图案并写入数字投影装置；远心摄像设备102可以为使用物像双远心镜头的摄像机，摄像机可以为电荷耦合器件、液晶器件、空间光调制器件、CMOS器件或数码相机；应用该测量系统测量物体的三维信息时，待测物体104放置于平移台103上，平移台103水平放置并且能上下移动；平移台103可以为电控平移台，用计算机控制步进距离的电动步进机装置；平移台103也可为手动控制移动的平移台。
图2为本发明一种远心三维形貌测量系统的标定方法的设备位置示意图，如图2所示，调节远心投影设备101、远心摄像设备102的相对位置，使平移台103处于远心投影设备101和远心摄像设备102的共同景深范围内，并确保远心投影设备101投射到平移台103上的结构光能被远心摄像设备102采集。为了简化图例，图2中远心投影设备101的物像双远心镜头分别用其主点P1、P2来示意投影 的光线，同样远心摄像设备102的物像双远心镜头分别用其主点C1、C2来示意光线的成像。
步骤S2：使平移台103处于远心投影设备101和远心摄像设备102的共同景深范围内，控制远心投影设备101对平移台103投射正弦条纹图，远心摄像设备102采集正弦条纹图，选取远心摄像设备102图像平面上的任一像素点作为标定用像素点，利用多步相移法解得该标定用像素点的绝对相位值，并记录此时的平移台103高度值；
控制平移台103在远心投影设备101和远心摄像设备102的共同景深范围内沿远心摄像设备102的光轴方向进行数次位移，在移动平移台103至不同高度时，获取此高度下标定用像素点的绝对相位值，并记录相应的平移台103高度值；
对获得的平移台103的高度值与相应的标定用像素点的绝对相位值进行线性拟合，建立远心成像的三维形貌测量系统中绝对相位值与平移台高度值的转换关系；
图3为本发明步骤S2的一具体实施例的流程示意图，如图3所示，在本实施例中，所述步骤S2，其具体包括：
步骤S21：控制所述平移台103在远心投影设备101和远心摄像设备102的共同景深范围内，调整平移台103使它处于高度测量范围的最低位置，记下平移台103的最低高度z0；
步骤S22：利用计算机编写周期为T0的正弦条纹图植入远心投影设备101，使远心投影设备101向平移台103投射周期恒定的四幅正弦条纹图；四幅正弦条纹图以第一幅正弦条纹图为基础分别进行了2πL/4(L＝0,1,2,3)的相移；远心摄像设备102按顺序采集四幅条纹图；选取远心摄像设备102图像平面上的任一像素点作为标定用像素点，设标定用像素点在远心摄像设备102的图像坐标系中的像素坐标为(μ,ν)，该像素点为平移台上点(x,y)处成像在摄像设备图像平面上的像素点，由于与本发明所述方法相配套的远心成像的三维形貌测量系统中投影设备101与摄像设备102均使用双侧远心镜头，在远心投影系统的景深范围内，投影设备投射到参考平面上的为周期恒定的正弦条纹图，因而平移台上点(x,y)处的绝对相位值与像素点(μ,ν)处的绝对相位值相等，且标定用像素点的光强IL(μ,ν)表达式为：
Figure PCTCN2015089903-appb-000017
其中L＝0,1,2,3，a(μ,ν)为背景光强，b(μ,ν)为条纹对比度，
Figure PCTCN2015089903-appb-000018
为标定用像素点(μ,ν)处的绝对相位值；
按照四步相移法，可求得标定用像素点(μ,ν)处的包裹相位为φ(μ,ν)：
Figure PCTCN2015089903-appb-000019
由于包裹相位的值域被切断在[-π,π]之间，须将其进行相位展开，得到标定用像素点(μ,ν)处绝对相位值
Figure PCTCN2015089903-appb-000020
为：
Figure PCTCN2015089903-appb-000021
其中k(μ,ν)＝±1；
步骤S23：图4为步骤S23中控制平移台在系统中移动的结构示意图，如图4所示，控制平移台103在远心投影设备101和远心摄像设备102的共同景深范围内沿远心摄像设备102的光轴方向等间距移动△z的距离，使平移台103处于zj＝z0+j△z(j＝0，1，2，……，n)的不同高度处，按照步骤S22的方法分别求得当平移台103处于zj(j＝0,1,2,……,n)的高度时标定用像素点(μ,ν)处绝对相位值
Figure PCTCN2015089903-appb-000022
步骤S24：对获得的平移台103的不同高度zj(j＝0,1,2,……,n)与相应的标定用像素点(μ,ν)的绝对相位值
Figure PCTCN2015089903-appb-000023
进行线性拟合；得到远心成像的三维形貌测量系统中绝对相位值与高度的线性转换关系式：
Figure PCTCN2015089903-appb-000024
其中M为线性比例因子，由于在三维形貌测量中往往得到的是受物体高度调制的相位差，因此只需关注线性关系中的线性比例因子的精度。
远心镜头具有在一定的物距范围内，使得到的图像放大倍率不会随物距的变化而变化的特性，因而在本发明远心成像的三维形貌测量系统中，只需求得在景深范围内标定用像素点处的绝对相位值与高度的线性转换关系，便可以将远心摄像设备图像上的任一像素点都运用这种关系去对应，简化了标定过程。
为更清楚表述本发明步骤S2远心成像的三维形貌测量系统中标定绝对相位值
Figure PCTCN2015089903-appb-000025
与高度z的转换关系式的过程，下面对本实施的具体实施方式做进一步说明。
本实施例中的远心摄像设备采用了大恒工业级CMOS摄像机DH-HV1351-UC，像素为1280×1024，镜头为大恒的物像双远心镜头GC0230105；远心投影设备采用了惠普的投影仪AX325AA，分辨率为800×600，镜头为大恒的物像双远心镜头GC0230106；平移台为手动控制上下移动的平移台，其移动精度为0.01mm。本实施例投影仪和摄像机的摆放位置如图2所示并保持一定夹角不变，控制平移台沿z轴在竖直方向上平移。投影仪向平移台倾斜投射垂直于x轴的正弦条纹图的周期为16pixel，投射的四幅正弦条纹图以第一幅正弦条纹图为基础产生2πL/4(L＝0,1,2,3)的相移；规定第一幅正弦条纹图的初相位为0，则摄像机按顺序采集的这四幅正弦条纹图可以表示为：
Figure PCTCN2015089903-appb-000026
其中L＝0,1,2,3，对每一个高度下的平移台投射这四幅等相位差的正弦条纹图，摄像机按顺序采集此四幅正弦条纹图，利用四步相移法即可得出摄像机图像平面上像素点(μ,ν)在每一个高度z下的绝对相位值
Figure PCTCN2015089903-appb-000027
本实施例中选择摄像机图像平面上索引为(710，571)的像素点，手动控制平移台每次向上移动0.05mm的距离，规定平移台所能达到的最低高度为0mm，标定高度范围为2.40mm至2.70mm。用四步相移法解得摄像机图像平面上索引为(710，571)的像素点的绝对相位值
Figure PCTCN2015089903-appb-000028
与平移台高度z的对应关系如下面表格所示：
Figure PCTCN2015089903-appb-000029
对这些数据进行线性拟合，拟合的结果如图5所示，图5为本发明步骤S2一具体实施中绝对相位值与平移台高度值的线性拟合曲线图。值得说明的是，本案例是为了避免进行相位展开这一操作，所标定的高度为2.40mm至2.70mm。实际上，本案例所搭建的远心成像的测量系统的高度测量范围高达5mm。
本发明还包括步骤S3，步骤S3：通过标定远心摄像设备的参量，将远心摄像设备图像平面上的像素坐标转换为世界坐标。
图6为本发明步骤S3的一具体实施例的流程示意图，如图6所示，在本实施例中步骤S3，其具体包括：
步骤S31、将平移台调整至远心投影设备与远心摄像设备的共同景深范围内，放置标定耙于平移台上，由远心投影设备向标定耙投射白光，远心摄像设备采集标定耙图像；对采集到的图像提取特征点，得到一系列世界坐标下特征点的世界坐标(Xωi,Yωi,Zωi)，与特征点成像在远心摄像设备 的图像坐标系上对应的一系列像素坐标(μi,νi)；
步骤S32、利用一系列特征点的世界坐标(Xωi,Yωi,Zωi)与像素坐标(μi,νi)的对应关系，标定远心摄像设备的参量，将远心摄像设备图像平面上的像素坐标(μ,ν)转换为世界坐标(Xω,Yω)。
图7为本发明步骤S32的一具体实施例的流程示意图，如图7所示，所述步骤S32，其具体包括：
步骤S321：在不考虑镜头畸变情况下，建立物像双远心镜头成像时的正射变换模型；所述物像双远心镜头成像时的正射变换模型为：
Figure PCTCN2015089903-appb-000030
其中，(xμi,yμi)为一系列特征点在所述远心摄像设备的成像平面坐标系中的图像坐标，(Xωi,Yωi,Zωi)为一系列特征点在世界坐标系中的世界坐标，m为物像双远心镜头的放大倍数，R＝[rij]为旋转矩阵，T＝[tx ty tz]T为平移矩阵，dμ和dν分别为每个像素在X轴、Y轴方向上的物理尺寸；
在不考虑镜头畸变情况下，所述远心摄像设备图像平面上的像素坐标与远心摄像设备成像平面上的图像坐标的对应关系为：
Figure PCTCN2015089903-appb-000031
其中(μ0,ν0)为远心摄像设备图像平面上的中心像素点坐标，也是成像平面上图像坐标的原点。
在本实施例中所采用的正射变换模型，其具体建立过程如下：
图8为具有远心透镜的摄像设备的成像模型示意图，本实施例中远心摄像设备的成像模型如图8所示，特征点P在世界坐标系下的坐标为(Xω,Yω,Zω)，p(Xc,Yc,Zc)是特征点P在远心摄像设备坐标系中的坐标；如果是理想的正投影模型，那么P(Xc,Yc,Zc)在成像平面坐标系中的理想图像坐标就是p(xu,yu)，由于镜头畸变，实际的图像坐标p(xd,yd)与理想图像坐标p(xu,yu)并不相同；(u,v)是远心摄像设备图像平面以像素为单位的像素坐标。
远心镜头进行缩放正投影，在不考虑镜头畸变情况下，任意的投影点P的理想(不失真)在成像平面的图像坐标与远心摄像设备坐标的转换关系表示为：
Figure PCTCN2015089903-appb-000032
其中m是远心透镜的有效放大倍数。
任意的投影点P的世界坐标与远心摄像设备坐标的关系表示为：
Figure PCTCN2015089903-appb-000033
其中，R＝[rij]是旋转矩阵，T＝[tx ty tz]是平移矩阵。
在不考虑任何畸变的情况下，成像平面坐标系xoy与远心摄像设备图像平面坐标系相一致，因此，从成像平面坐标(xu,yu)转换成像素坐标(u,v)的表达式为：
Figure PCTCN2015089903-appb-000034
其中du和dv分别是一个像素在x和y方向上的物理尺寸，(μ0,ν0)为远心摄像设备图像平面上的中心像素点坐标，也是成像平面上图像坐标的原点。
结合式(5-a)-(5-c)，远心透镜的正投影形成并通过以下等式表示：
Figure PCTCN2015089903-appb-000035
式(5-d)即为物像双远心镜头成像时的正射变换模型。
步骤S322：考虑所述远心摄像设备的镜头畸变，镜头畸变主要有三种类型：径向畸变，偏心畸变和薄棱镜畸变；在本实施例中考虑有效的失真，镜头畸变的表达式为：
Figure PCTCN2015089903-appb-000036
其中，
Figure PCTCN2015089903-appb-000037
为每个像素在X轴方向上的畸变参数，
Figure PCTCN2015089903-appb-000038
为每个像素在Y轴方向上的畸变参数；k1为径向畸变程度的参数，h1、h2为离心畸变程度的参数，s1、s2为薄棱镜畸变程度的参数；
建立所述远心摄像设备图像平面上的像素坐标(μi,νi)与远心摄像设备成像平面上的图像坐标(xμi,yμi)的对应关系：
Figure PCTCN2015089903-appb-000039
其中(μ0,ν0)为远心摄像设备图像平面上的中心像素点坐标，也是成像平面上图像坐标的原点。
步骤S323：所述远心摄像设备的参量包括外参数旋转矩阵R、平移矩阵T以及物像双远心镜头的放大倍数参数m的初值；
由所述一系列特征点的世界坐标(Xωi,Yωi,Zωi)和对应的一系列像素坐标(μi,νi)根据式 (5)、(6)求在不考虑畸变的情况下远心摄像设备的外参数R、T以及物像双远心镜头的放大倍数参数m的初值；
再将式(8)中用图像坐标表示的像素坐标带入式(5)中求远心摄像设备的内参数k1、h1、h1、s1、s2的初值；
由远心摄像设备的内外参数初值、物像双远心镜头的放大倍数参数m的初值和特征点的像素坐标(μi,νi)，反求得到考虑了镜头畸变的一系列特征点的世界坐标
Figure PCTCN2015089903-appb-000040
建立目标函数：
Figure PCTCN2015089903-appb-000041
其中，N为特征点总数，通过最小二乘法精确得到所述远心摄像设备外参数m、R、T和内参数k1、h1、h2、s1、s2；
步骤S324：根据得到的所述远心摄像设备外参数R、T和内参数k1、h1、h2、s1、s2以及物像双远心镜头的放大倍数参数m，将所述远心摄像设备图像平面上的像素坐标(μ,ν)转换为世界坐标(Xω,Yω)。
以上所述实施步骤和方法仅仅表达了本发明的一种实施方式，描述较为具体和详细，但并不能因此而理解为对本发明专利范围的限制。在不脱离本发明专利构思的前提下，所作的变形和改进应当都属于本发明专利的保护范围。

Claims (4)

  1. 一种远心成像的三维形貌测量系统标定方法，其特征在于：所述标定方法包括如下步骤：
    步骤S1:搭建远心三维形貌测量系统，所述测量系统包括：远心投影设备、远心摄像设备、平移台；远心摄像设备的光轴垂直于水平放置的平移台，远心投影设备的光轴与平移台成一夹角，并控制远心摄像设备的光轴与远心投影设备的光轴处于同一平面内；
    步骤S2：使平移台处于远心投影设备和远心摄像设备的共同景深范围内，控制远心投影设备对平移台投射正弦条纹图，远心摄像设备采集所述正弦条纹图，选取远心摄像设备图像平面上的任一像素点作为标定用像素点，利用多步相移法解得该标定用像素点的绝对相位值，并记录此时的平移台高度值；
    控制平移台在远心投影设备和远心摄像设备的共同景深范围内沿远心摄像设备的光轴方向进行数次位移，在移动平移台至不同高度时，获取此高度下标定用像素点的绝对相位值，并记录相应的平移台高度值；
    对获得的平移台的高度值与相应的标定用像素点的绝对相位值进行线性拟合，建立远心成像的三维形貌测量系统中绝对相位值与平移台高度值的转换关系；
    步骤S3：通过标定远心摄像设备的参量，将远心摄像设备图像平面上的像素坐标转换为世界坐标。
  2. 根据权利要求1所述一种远心成像的三维形貌测量系统标定方法，其特征在于：所述步骤S2，其具体包括：
    步骤S21：控制所述平移台在所述远心投影设备和远心摄像设备的共同景深范围内，调整所述平移台使它处于高度测量范围的最低位置，记下平移台的最低高度z0；
    步骤S22：利用计算机编写周期为T0的正弦条纹图植入所述远心投影设备，使所述远心投影设备向所述平移台投射周期恒定的四幅正弦条纹图；所述四幅正弦条纹图以第一幅正弦条纹图为基础分别进行了2πL/4(L＝0,1,2,3)的相移；所述远心摄像设备按顺序采集四幅条纹图；选取所述远心摄像设备图像平面上的任一像素点作为标定用像素点，设所述标定用像素点在所述远心摄像设备的图像坐标系中的像素坐标为(μ,ν)；所述标定用像素点的光强IL(μ,ν)表达式为：
    Figure PCTCN2015089903-appb-100001
    其中L＝0,1,2,3，a(μ,ν)为背景光强，b(μ,ν)为条纹对比度，
    Figure PCTCN2015089903-appb-100002
    为标定用像素点(μ,ν)处的绝对相位值；
    按照四步相移法，可求得所述标定用像素点(μ,ν)处的包裹相位为φ(μ,ν)：
    Figure PCTCN2015089903-appb-100003
    由于包裹相位的值域被切断在[-π,π]之间，须将其进行相位展开，得到所述标定用像素点(μ,ν)处绝对相位值
    Figure PCTCN2015089903-appb-100004
    为：
    Figure PCTCN2015089903-appb-100005
    其中k(μ,ν)＝±1；
    步骤S23：控制所述平移台在所述远心投影设备和远心摄像设备的共同景深范围内沿所述远心摄像设备的光轴方向等间距移动△z的距离，使所述平移台处于zj＝z0+j△z(j＝0，1，2，……，n)的不同高度处，按照所述步骤S22的方法分别求得当平 移台处于zj(j＝0,1,2,……,n)的高度时标定用像素点(μ,ν)处绝对相位值
    Figure PCTCN2015089903-appb-100006
    步骤S24：对获得的平移台的不同高度zj(j＝0,1,2,……,n)与相应的标定用像素点(μ,ν)的绝对相位值
    Figure PCTCN2015089903-appb-100007
    进行线性拟合；得到远心成像的三维形貌测量系统中绝对相位值与高度的线性转换关系式：
    Figure PCTCN2015089903-appb-100008
    其中M为线性比例因子。
  3. 根据权利要求1所述一种远心成像的三维形貌测量系统标定方法，其特征在于：
    所述步骤S3，其具体包括：
    步骤S31：将所述平移台调整至所述远心投影设备与远心摄像设备的共同景深范围内，放置标定耙于所述平移台上，由所述远心投影设备向标定耙投射白光，所述远心摄像设备采集标定耙图像；对采集到的图像提取特征点，得到一系列世界坐标下特征点的世界坐标(Xωi,Yωi,Zωi)，与特征点成像在所述远心摄像设备的图像坐标系上对应的一系列像素坐标(μi,νi)；
    步骤S32：利用一系列特征点的世界坐标(Xωi,Yωi,Zωi)与像素坐标(μi,νi)的对应关系，标定所述远心摄像设备的参量，将所述远心摄像设备图像平面上的像素坐标(μ,ν)转换为世界坐标(Xω,Yω)。
  4. 根据权利要求3所述一种远心成像的三维形貌测量系统标定方法，其特征在于：
    所述步骤S32，其具体包括：
    步骤S321：在不考虑镜头畸变情况下，建立物像双远心镜头成像时的正射变换模型；所述物像双远心镜头成像时的正射变换模型为：
    Figure PCTCN2015089903-appb-100009
    其中，(xμi,yμi)为一系列特征点在所述远心摄像设备的成像平面坐标系中的图像坐标，(Xωi,Yωi,Zωi)为一系列特征点在世界坐标系中的世界坐标，m为物像双远心镜头的放大倍数，R＝[rij]为旋转矩阵，T＝[tx ty tz]T为平移矩阵，dμ和dν分别为每个像素在X轴、Y轴方向上的物理尺寸；
    在不考虑镜头畸变情况下，所述远心摄像设备图像平面上的像素坐标与远心摄像设备成像平面上的图像坐标的对应关系为：
    Figure PCTCN2015089903-appb-100010
    其中(μ0,ν0)为远心摄像设备图像平面上的中心像素点坐标，也是成像平面上图像坐标的原点；
    步骤S322：考虑所述远心摄像设备的镜头畸变，所述镜头畸变的表达式为：
    Figure PCTCN2015089903-appb-100011
    其中，
    Figure PCTCN2015089903-appb-100012
    为每个像素在X轴方向上的畸变参数，
    Figure PCTCN2015089903-appb-100013
    为每个像素在Y轴方向上的畸变参数；k1为径向畸变程度的参数，h1、h2为离心畸变程度的参数，s1、s2为薄棱镜畸变程度的参数；
    建立所述远心摄像设备图像平面上的像素坐标(μi,νi)与远心摄像设备成像平面上的图像坐标(xμi,yμi)的对应关系：
    Figure PCTCN2015089903-appb-100014
    其中(μ0,ν0)为远心摄像设备图像平面上的中心像素点坐标也是成像平面上图像坐标的原点；
    步骤S323：所述远心摄像设备的参量包括外参数旋转矩阵R、平移矩阵T以及物像双远心镜头的放大倍数参数m的初值；
    由所述一系列特征点的世界坐标(Xωi,Yωi,Zωi)和对应的一系列像素坐标(μi,νi)根据式(5)、(6)求在不考虑畸变的情况下远心摄像设备的外参数R、T以及物像双远心镜头的放大倍数参数m的初值；
    再将式(8)中用图像坐标表示的像素坐标带入式(5)中求远心摄像设备的内参数k1、h1、h1、s1、s2的初值；
    由远心摄像设备的内外参数初值、物像双远心镜头的放大倍数参数m的初值和特征点的像素坐标(μi,νi)，反求得到考虑了镜头畸变的一系列特征点的世界坐标
    Figure PCTCN2015089903-appb-100015
    建立目标函数：
    Figure PCTCN2015089903-appb-100016
    其中，N为特征点总数，通过最小二乘法求得所述远心摄像设备外参数R、T和内参数k1、h1、h2、s1、s2以及物像双远心镜头的放大倍数参数m的精确值；
    步骤S324：根据得到的所述远心摄像设备外参数R、T和内参数k1、h1、h2、s1、s2以及物像双远心镜头的放大倍数参数m，将所述远心摄像设备图像平面上的像素坐标(μ,ν)转换为世界坐标(Xω,Yω)。
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