WO2018040017A1 - 一种基于自适应条纹的投影仪镜头畸变校正方法及其系统 - Google Patents

一种基于自适应条纹的投影仪镜头畸变校正方法及其系统 Download PDF

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WO2018040017A1
WO2018040017A1 PCT/CN2016/097664 CN2016097664W WO2018040017A1 WO 2018040017 A1 WO2018040017 A1 WO 2018040017A1 CN 2016097664 W CN2016097664 W CN 2016097664W WO 2018040017 A1 WO2018040017 A1 WO 2018040017A1
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phase
plane
projector
stripe
adaptive
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PCT/CN2016/097664
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English (en)
French (fr)
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彭翔
彭军政
刘晓利
邓定南
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深圳大学
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Priority to PCT/CN2016/097664 priority Critical patent/WO2018040017A1/zh
Priority to CN201680000846.2A priority patent/CN106461380B/zh
Publication of WO2018040017A1 publication Critical patent/WO2018040017A1/zh

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00—Image enhancement or restoration
    • G06T5/80—Geometric correction
    • 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

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  • the invention relates to the field of optical three-dimensional measurement, and in particular to a method and a system for correcting a lens distortion of a projector based on an adaptive stripe.
  • Stripe projection profilometry as a branch of optical 3D measurement technology, has been made in the fields of industrial manufacturing, medical diagnosis, cultural heritage, film and television entertainment, etc. due to its non-contact, full field, rapidity and high resolution.
  • An increasingly widespread application is: using a projector to project a series of carrier frequency fringe patterns on the surface of the object to be tested (such as a sinusoidal fringe pattern), the depth information of the object to be measured is modulated by the fringe pattern to be deformed, and then utilized.
  • the stripe analysis technique performs phase demodulation on the deformed fringe pattern acquired by the camera to obtain the phase map containing the depth information of the object to be measured.
  • the depth map of the object to be measured can be obtained from the phase map.
  • the quality of the phase map is one of the key factors determining the accuracy of the three-dimensional measurement result.
  • lens distortion errors of projectors and cameras are unavoidable due to manufacturing and assembly errors.
  • the lens distortion of the projector will distort the projected sinusoidal fringe pattern—i.e., a variable-period fringe pattern will be obtained on a plane perpendicular to the optical axis of the projector.
  • the phase of the demodulation will introduce a deformation phase due to the lens distortion of the projector, resulting in the final
  • the three-dimensional measurement results in errors.
  • the lens distortion of the projector brings measurement error.
  • Most of the existing methods first calibrate the projector, and then modify the fringe pattern to be projected according to the calibrated lens distortion coefficient, so that the fringe pattern after projection by the projector is a standard sine. stripe.
  • the existing calibration method usually assumes that the re-projection error of the projection plane satisfies the normal distribution, and uses the maximum likelihood estimation method to calibrate the internal and external parameters of the projector.
  • the mapping relationship between the camera image plane and the projection plane is nonlinear, The re-projection error with statistical properties cannot be obtained on the projection plane. In this case, there is a certain error in using the maximum likelihood estimation method to calibrate the internal and external parameters of the projector.
  • an object of the present invention is to provide a method and system for correcting lens distortion of a projector based on adaptive stripe, which aims to solve the problem that the accuracy of lens distortion correction of the projector in the prior art is low and difficult to operate.
  • the invention provides a lens distortion correction method based on adaptive stripe, which mainly comprises:
  • Step 1 Using a fringe projection measurement system to obtain an absolute phase of the standard panel
  • Step two calculating a phase error caused by lens distortion of the projector according to the absolute phase
  • Step 3 defining a plane G perpendicular to the optical axis of the projector lens, and calculating a mapping relationship between the plane G and the projection plane according to the phase error;
  • Step 4 According to the mapping relationship, generate frequency conversion and phase shift adaptive stripes for projection, so that the stripes cast by the projector are standard sinusoidal stripes on the plane G.
  • the present invention also provides an adaptive stripe-based projector lens distortion correction system, the system comprising:
  • phase acquisition module for acquiring an absolute phase of a standard panel using a stripe projection measurement system
  • An error calculation module configured to calculate a phase error caused by a lens distortion of the projector according to the absolute phase
  • a mapping calculation module configured to define a plane G perpendicular to an optical axis of the projector lens, and calculate a mapping relationship between the plane G and the projection plane according to the phase error;
  • a stripe generating module configured to generate a variable frequency and phase shift adaptive stripe for projection according to the mapping relationship, so that the stripe projected by the projector is a standard sinusoidal stripe on the plane G.
  • the technical solutions provided by the present invention have significant advantages including: (1) the invention does not need to directly calibrate the projector, avoids the influence of the calibration error on the measurement result, can improve the measurement accuracy, and reduces the computational complexity; (2) The invention does not need to change the spatial orientation and posture of the flat plate multiple times, and only needs to place the standard flat plate once in the measurement space range once, so that adaptive stripes can be generated for projection, which can shorten the time for preparation in advance; (3) The invention does not need to calculate the parameters of the measurement system, such as the angle between the projector and the optical axis of the camera, etc., and can be applied to an arbitrary set of stripe projection measurement systems.
  • FIG. 1 is a flowchart of a method for correcting a lens distortion of a projector based on an adaptive stripe according to an embodiment of the present invention
  • FIG. 2 is a schematic diagram showing the internal structure of a lens distortion correction system 10 based on an adaptive stripe according to an embodiment of the present invention
  • FIG. 3 is a schematic diagram showing the result of using a adaptive stripe measurement standard panel according to an embodiment of the present invention.
  • FIG. 4 is a schematic diagram of measurement results of a standard sphere using adaptive stripe measurement according to an embodiment of the present invention.
  • FIG. 5 is a schematic diagram showing a redefinition error distribution of a projector and a camera calibration according to an embodiment of the present invention
  • FIG. 6 is a schematic diagram showing measurement results of a ceramic plane after the projector is calibrated by the phase assist method according to an embodiment of the present invention.
  • the invention adopts the following technical scheme: firstly, the standard flat panel is measured by using the stripe projection measurement system (example) Absolute phase such as flatness less than 0.01mm); secondly, calculate the phase error caused by the lens distortion of the projector according to the absolute phase of the measurement; then define a plane G perpendicular to the optical axis of the projector lens, and establish a plane according to the phase error The mapping relationship between G and the projection plane; finally, using the established mapping relationship to generate adaptive stripes for projection, the effect of the lens distortion of the projector on the fringe pattern can be cancelled, and the standard sinusoidal stripe can be obtained on the plane G.
  • the stripe projection measurement system example
  • Absolute phase such as flatness less than 0.01mm
  • This method eliminates the need to calibrate the projector and measurement system parameters, such as the lens distortion coefficient of the projector, the angle between the projector and the optical axis of the camera, etc., which can reduce the computational complexity and improve the accuracy of the measurement results, and is suitable for arbitrary settings.
  • Stripe projection measurement system This method eliminates the need to calibrate the projector and measurement system parameters, such as the lens distortion coefficient of the projector, the angle between the projector and the optical axis of the camera, etc.
  • FIG. 1 is a flowchart of a method for correcting a lens distortion of a projector based on an adaptive stripe according to an embodiment of the present invention.
  • step one uses the fringe projection measurement system to obtain the absolute phase of the standard panel.
  • step one specifically includes:
  • Projector is used to project a set of vertical and horizontal frequency conversion and phase-shifted sinusoidal fringe patterns to the standard plate. Then, the stripe analysis technique is used to analyze the sine fringe pattern recorded by the camera, and the absolute phase of the standard plate is obtained ( ⁇ m, h , ⁇ m,v ).
  • a standard flat plate is arbitrarily placed in the measurement space of the stripe projection system, and a set of horizontal and vertical sinusoidal fringe patterns of the frequency conversion and phase shift are respectively projected onto the flat plate by the projector.
  • the amount of phase shift between N and N represents the number of phase shifts.
  • the wrap phase ⁇ w can be calculated by the following formula:
  • step S2 step two, based on the absolute phase, calculates a phase error due to lens distortion of the projector.
  • the step 2 specifically includes:
  • the absolute phase of the panel can be expressed by the following formula ⁇ c (i, j) represents the carrier phase fitted at the pixel point (i, j), and r, s, t, u, v represent the coefficients associated with the system parameters.
  • ⁇ c (i, j) represents the carrier phase fitted at the pixel point (i, j)
  • r, s, t, u, v represent the coefficients associated with the system parameters.
  • the measurement results of the absolute phase of the standard flat panel include three parts: the carrier phase due to the stripe projection measurement system setting, and the projection by the projection Phase error caused by lens distortion error of the instrument and camera. Because the camera calibration method is very mature and accurate.
  • the pre-processing of the acquired fringe pattern according to the camera calibration result can eliminate the influence of the camera lens distortion on the measurement phase.
  • the lens distortion of the projector is usually very small, and it is difficult to directly detect the deformation of the projected fringe pattern by naked eye observation.
  • a carrier phase distribution can be obtained.
  • phase errors ( ⁇ a, h , ⁇ a, v ) due to lens distortion of the projector after projecting the horizontal and vertical phase shifting stripes.
  • step S3 step three defines a plane G perpendicular to the optical axis of the projector lens, and calculates a mapping relationship between the plane G and the projection plane according to the phase error.
  • the step 3 specifically includes:
  • the mapping relationship between the phase point pairs between the projection plane and the camera image plane is established as Where (s 1 , t 1 ) is a pixel point on the projection plane, and the phase of the (s 1 , t 1 ) pixel point is equal to the phase of the pixel point (i, j) on the camera image plane;
  • phase error ( ⁇ a,h , ⁇ a,v ) obtained in step 2
  • a three-dimensional data point set (s 1 , t 1 , ⁇ a, h (i, j)) and (s 1 , t 1 , ⁇ ) are established.
  • the two three-dimensional data point sets (s 1 , t 1 , ⁇ a, h (i, j)) and (s 1 , t 1 , ⁇ a, v (i, j) are fitted using Zernike Polynomials. )), calculating the phase error ( ⁇ a, h (s, t), ⁇ a, v (s, t)) of the integer pixel point (s, t) on the projection plane according to the fitted coefficient;
  • step S4 according to the mapping relationship, variable frequency and phase shift adaptive stripes are generated for projection, so that the stripes cast by the projector are standard sinusoidal stripes on the plane G.
  • the step 4 specifically includes:
  • the invention provides an adaptive stripe-based projector lens distortion correction method, which firstly obtains the absolute phase of the standard plate, and then uses the absolute phase to calculate the phase error caused by the lens distortion of the projector, and then defines the optical axis perpendicular to the projector.
  • a certain plane G uses the phase error to establish the mapping relationship between the plane G and the projection plane.
  • an adaptive fringe pattern is generated for projection, that is, the influence of the lens distortion of the projector on the fringe pattern is
  • a standard sinusoidal fringe pattern is obtained on plane G.
  • This method eliminates the need to calibrate the projector and measurement system parameters, such as the lens distortion coefficient of the projector, the angle between the projector and the optical axis of the camera, etc., which can reduce the computational complexity and improve the accuracy of the measurement results, and is suitable for arbitrary settings.
  • Stripe projection measurement system This method eliminates the need to calibrate the projector and measurement system parameters, such as the lens distortion coefficient of the projector, the angle between the projector and the optical axis of the camera, etc.
  • FIG. 2 a schematic diagram of a structure of a lens distortion correction system 10 based on an adaptive stripe according to an embodiment of the present invention is shown.
  • the adaptive lens based lens distortion correction system 10 mainly includes a phase acquisition module 11 , an error calculation module 12 , a mapping calculation module 13 , and a stripe generation module 14 .
  • the phase acquisition module 11 is configured to acquire the absolute phase of the standard panel by using the stripe projection measurement system.
  • phase acquiring module 11 is specifically configured to:
  • a vertical and horizontal variable frequency and phase-shifted sinusoidal fringe pattern is projected onto the standard panel by the projector, and then the sine fringe pattern recorded by the camera is analyzed by the stripe analysis technique, and the absolute phase of the standard plate is obtained ( ⁇ m, h , ⁇ m,v ).
  • a standard flat plate is arbitrarily placed in the measurement space of the stripe projection system, and a set of horizontal and vertical sinusoidal fringe patterns of the frequency conversion and phase shift are respectively projected onto the flat plate by the projector.
  • the amount of phase shift between N and N represents the number of phase shifts.
  • the wrap phase ⁇ w can be calculated by the following formula:
  • the error calculation module 12 is configured to calculate a phase error caused by lens distortion of the projector according to the absolute phase.
  • the error calculation module 12 is specifically configured to:
  • the absolute phase of the panel can be expressed by the following formula ⁇ c (i, j) represents the carrier phase fitted at the pixel point (i, j), and r, s, t, u, v represent the coefficients associated with the system parameters.
  • ⁇ c (i, j) represents the carrier phase fitted at the pixel point (i, j)
  • r, s, t, u, v represent the coefficients associated with the system parameters.
  • the measurement results of the absolute phase of the standard flat panel include three parts: the carrier phase due to the stripe projection measurement system setting, and the projection by the projection Phase error caused by lens distortion error of the instrument and camera. Because the camera calibration method is very mature and accurate.
  • the pre-processing of the acquired fringe pattern according to the camera calibration result can eliminate the influence of the camera lens distortion on the measurement phase.
  • the lens distortion of the projector is usually very small, and it is difficult to directly detect the deformation of the projected fringe pattern by naked eye observation.
  • a carrier phase distribution can be obtained.
  • phase errors ( ⁇ a, h , ⁇ a, v ) due to lens distortion of the projector after projecting the horizontal and vertical phase shifting stripes.
  • the mapping calculation module 13 is configured to define a plane G perpendicular to the optical axis of the projector lens, and calculate a mapping relationship between the plane G and the projection plane according to the phase error.
  • mapping calculation module 13 is specifically configured to:
  • the stripe generating module 14 is configured to generate a variable frequency and phase shift adaptive stripe for projection according to the mapping relationship, so that the stripe projected by the projector is a standard sinusoidal stripe on the plane G.
  • the stripe generation module 14 is specifically configured to:
  • the invention provides an adaptive stripe-based projector lens distortion correction system 10, which does not need to calibrate the projector and the measurement system parameters, such as the lens distortion coefficient of the projector, the angle between the projector and the optical axis of the camera, etc. Reduce the computational complexity and improve the accuracy of measurement results, suitable for arbitrarily set stripe projection measurement systems.
  • a ceramic plate flatness less than 0.01 mm was measured.
  • a set of frequency conversion (13, 14, 15 pixels with stripe width) and phase shift (four-step phase shift) adaptive stripes are generated by the method of the invention, and then sequentially projected onto a standard tablet and passed through the camera.
  • the fringe pattern is recorded and the fringe image is processed using the stripe analysis technique.
  • Figure 3(a) shows the residual distribution after the actual measured phase minus the carrier phase
  • Figure 3(b) shows the reconstructed plate. 3D data.
  • the least squares fitting algorithm is used to fit the measurement results of the plate, and FIG.
  • 3(c) is the deviation distribution of the measured three-dimensional data and the fitting result.
  • a standard phase-shifted sinusoidal fringe pattern is generated by a computer and projected onto a ceramic plate for measurement.
  • Figure 3(d) shows the phase error recovered after projecting a standard sinusoidal phase-shifted fringe pattern. It can be seen from the figure that the lens distortion of the projector will cause the projected fringe pattern to be deformed, so that there is an error in the phase recovery result, which affects the accuracy of the three-dimensional reconstruction result, and the method of the invention can effectively suppress the lens distortion of the projector to the fringe pattern. The impact of obtaining accurate 3D reconstruction results.
  • the ceramic plates are randomly placed at 11 different positions, and at each position, the adaptive fringe pattern is projected onto the ceramic plate by the method of the present invention, and the three-dimensional reconstruction is reconstructed.
  • the measurement results are finally calculated using a least squares fitting algorithm to calculate the deviation between the measured data and the fitting result.
  • Table 1 counts the PV (Peak to Valley) value and the RMS (Root-mean-square) value of the deviation of the 11 measurement results.
  • the method of the present invention is capable of obtaining stable measurement results in the system measurement space.
  • the ceramic plate was mounted on a high-precision moving rail (with a resolution of 1.25 ⁇ m) through which the ceramic plates were respectively moved at different positions.
  • an adaptive fringe pattern is projected onto the ceramic panel using the method of the present invention, and the three-dimensional measurement results are reconstructed.
  • Figure 4 shows the measurement results of a section line profile in the center of the ceramic plate.
  • the reconstruction error using the method of the present invention is ⁇ 0.1 mm.
  • FIG. 5 shows the re-projection error of the projector and camera calibration results. It can be seen from the figure that the re-projection error of the projector calibration result is larger than the re-projection error of the camera calibration result. This result proves that the projector calibration method is fine. The degree is significantly lower than the calibration accuracy of the camera.
  • Figure 6 shows the deviation distribution of the reconstructed three-dimensional data and the least squares fitting result. The PV and RMS values of the reconstruction result error are known from the figure.
  • the reconstruction error of the edge region in the figure is obviously larger than that of the central region. This is mainly because there is a certain error in the calibration result of the projector. It is assumed that the distance between the actual image point and the center point of the image surface is d, when the nonlinear distortion model is used to calculate When the actual image point corresponds to the ideal image point, the calculation error increases with the increase of d, and finally the accuracy of the edge reconstruction result is significantly lower than the central region.
  • the above measurement results indirectly prove that the proposed method can effectively suppress the lens distortion error of the projector and improve the accuracy of the three-dimensional reconstruction result.
  • each unit included is only divided according to functional logic, but is not limited to the above division, as long as the corresponding function can be implemented; in addition, the specific name of each functional unit is also They are only used to facilitate mutual differentiation and are not intended to limit the scope of the present invention.

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Abstract

本发明提供一种基于自适应条纹的投影仪镜头畸变校正方法，其中，所述方法包括：利用条纹投影测量系统获取标准平板的绝对相位；根据所述绝对相位，计算由于投影仪的镜头畸变引起的相位误差；定义垂直于投影仪镜头光轴的一平面G，根据所述相位误差计算平面G与投影平面的映射关系；根据所述映射关系，生成变频、相移自适应条纹用于投影，使得投影仪投出的条纹在平面G上为标准的正弦条纹。本发明还提供一种基于自适应条纹的投影仪镜头畸变校正系统。本发明提供的技术方案能够改善测量精度、降低了计算复杂度，能够缩短前期准备的时间，能够适用于任意设置的条纹投射测量系统。

Description

一种基于自适应条纹的投影仪镜头畸变校正方法及其系统 技术领域
本发明涉及光学三维测量领域，尤其涉及一种基于自适应条纹的投影仪镜头畸变校正方法及其系统。
背景技术
条纹投影轮廓术，作为光学三维测量技术的分支，由于具有非接触性、全场性、快速性、高分辨率等特点，使其在工业制造、医学诊断、文化遗产、影视娱乐等领域得到了日益广泛的应用。它的工作原理是：利用投影仪向待测物体表面投射一系列的载频条纹图(如通常为正弦条纹图)，待测物体的深度信息会对条纹图调制而使之发生变形，然后利用条纹分析技术对相机采集的变形条纹图进行相位解调即可获得包含待测物体深度信息的相位图，最后根据标定好的相位深度映射关系即可由相位图求得待测物体的深度分布，实现对待测物体表面形貌的三维测量。
然而，由于待测物体的三维形貌是根据相位计算获得，相位图的质量是决定三维测量结果精度的关键因素之一。而在实际测量系统中，由于制造和装配误差，投影仪和相机的镜头畸变误差是不可避免。在这种情况下，投影仪的镜头畸变将会使得投射的正弦条纹图变形——即在垂直于投影仪光轴的平面上会得到变周期的条纹图。与定周期的条纹图(如正弦条纹图)相比较，如果将这种条纹图投射到待测物体表面，解调的相位中将会引入由于投影仪的镜头畸变引起的变形相位，导致最后的三维测量结果产生误差。
目前，针对投影仪的镜头畸变带来测量误差，现有方法大多先标定投影仪，然后根据标定的镜头畸变系数修改待投影的条纹图，使经过投影仪投射后的条纹图分布是标准的正弦条纹。然而，由于投影仪不能直接采集图像，精确地标 定投影仪仍然存在一定难度。此外，现有标定方法通常假定投影平面的重投影误差满足正态分布，采用极大似然估计法标定投影仪的内外部参数，然而，由于相机像面与投影平面之间映射关系是非线性，在投影平面上无法获得具有统计特性的重投影误差，在这种情况，采用极大似然估计法标定投影仪的内外参数存在一定的误差。
因此，如何实现高精度、易操作的投影仪镜头畸变校正成为条纹投影轮廓术中的一项技术难题，亟待解决。
发明内容
有鉴于此，本发明的目的在于提供一种基于自适应条纹的投影仪镜头畸变校正方法及其系统，旨在解决现有技术中投影仪镜头畸变校正的精度较低且不易操作的问题。
本发明提出一种基于自适应条纹的投影仪镜头畸变校正方法，主要包括：
步骤一、利用条纹投影测量系统获取标准平板的绝对相位；
步骤二、根据所述绝对相位，计算由于投影仪的镜头畸变引起的相位误差；
步骤三、定义垂直于投影仪镜头光轴的一平面G，根据所述相位误差计算平面G与投影平面的映射关系；
步骤四、根据所述映射关系，生成变频、相移自适应条纹用于投影，使得投影仪投出的条纹在平面G上为标准的正弦条纹。
另一方面，本发明还提供一种基于自适应条纹的投影仪镜头畸变校正系统，所述系统包括：
相位获取模块，用于利用条纹投影测量系统获取标准平板的绝对相位；
误差计算模块，用于根据所述绝对相位，计算由于投影仪的镜头畸变引起的相位误差；
映射计算模块，用于定义垂直于投影仪镜头光轴的一平面G，根据所述相位误差计算平面G与投影平面的映射关系；
条纹生成模块，用于根据所述映射关系，生成变频、相移自适应条纹用于投影，使得投影仪投出的条纹在平面G上为标准的正弦条纹。
本发明提供的技术方案与现有技术相比，其显著优点包括：(1)本发明无需直接标定投影仪，避免了标定误差对测量结果的影响，能够改善测量精度、降低了计算复杂度；(2)本发明无需多次改变平板的空间方位和姿态，只需将标准平板任意摆放在测量空间范围内一次，即可生成自适应条纹用于投影，能够缩短前期准备的时间；(3)本发明无需计算测量系统的参数，如投影仪和相机光轴之间的夹角等，能够适用于任意设置的条纹投射测量系统。
附图说明
图1为本发明一实施方式中基于自适应条纹的投影仪镜头畸变校正方法流程图；
图2为本发明一实施方式中基于自适应条纹的投影仪镜头畸变校正系统10的内部结构示意图；
图3为本发明一实施方式中利用自适应条纹测量标准平板的结果示意图；
图4为本发明一实施方式中利用自适应条纹测量标准球的测量结果示意图；
图5为本发明一实施方式中投影仪和相机标定的重投影误差分布示意图；
图6为本发明一实施方式中利用相位辅助法标定投影仪后对陶瓷平面的测量结果示意图。
具体实施方式
为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。
本发明采用如下技术方案：首先利用条纹投射测量系统测量标准平板(例 如平面度小于0.01mm)的绝对相位；其次根据测量的绝对相位，计算由投影仪的镜头畸变引起的相位误差；接着定义垂直于投影仪镜头光轴的某一平面G，根据相位误差建立平面G与投影平面之间的映射关系；最后利用所建立的映射关系，生成自适应条纹用于投影，即可抵消投影仪镜头畸变对条纹图的影响，在平面G上获得标准的正弦条纹。这种方法无需标定投影仪和测量系统参数，如投影仪的镜头畸变系数、投影仪和相机光轴之间的夹角等，能够降低计算复杂度、改善测量结果的精度，适用于任意设置的条纹投射测量系统。
以下将对本发明所提供的一种基于自适应条纹的投影仪镜头畸变校正方法进行详细说明。
请参阅图1，为本发明一实施方式中基于自适应条纹的投影仪镜头畸变校正方法流程图。
在步骤S1中，步骤一、利用条纹投影测量系统获取标准平板的绝对相位。
在本实施方式中，所述步骤一具体包括：
利用投影仪向标准平板分别投射一套竖直和水平的变频、相移正弦条纹图，然后采用条纹分析技术分析相机记录的正弦条纹图，并获得标准平板的绝对相位(Φm，h，Φm，v)。
在本实施方式中，将标准平板任意放置在条纹投射系统的测量空间内，利用投影仪向平板分别投射一套变频、相移的水平和竖直正弦条纹图。假设利用相机记录的第k帧条纹图强度
Figure PCTCN2016097664-appb-000001
可表示为
Figure PCTCN2016097664-appb-000002
其中，I′(i，j)表示平均强度，I″(i，j)表示调制度，Φ(i，j)表示待求的相位，δk＝2πN/k表示相邻两帧条纹图之间的相移量，N表示相移次数。根据相移算法，包裹相位Φw可由下式计算求得：
Figure PCTCN2016097664-appb-000003
其中，利用相位解包裹算法对Φw展开，可获得待测平板的两个绝对相位Φm，h和Φm，v。
在步骤S2中，步骤二、根据所述绝对相位，计算由于投影仪的镜头畸变引起的相位误差。
在本实施方式中，所述步骤二具体包括：
利用公式
Figure PCTCN2016097664-appb-000004
拟合测量的绝对相位获得载波相位分布，其中，Φc(i，j)表示在像素点(i，j)处拟合的载波相位，r，s，t，u，v表示与系统参数相关的系数；
然后将测量的绝对相位(Φm，h，Φm，v)减去拟合的载波相位Φc(i，j)，即可获得由于投影仪的镜头畸变引起的相位误差(ΔΦa，h，ΔΦa，v)。
在本实施方式中，假设忽略投影仪和相机的镜头畸变影响，则平板的绝对相位可用如下公式表示
Figure PCTCN2016097664-appb-000005
Φc(i，j)表示在像素点(i，j)处拟合的载波相位，r，s，t，u，v表示与系统参数相关的系数。然而，对于实际的条纹投射系统，投影仪和相机的镜头畸变对测量结果的影响不可忽略，标准平板绝对相位的测量结果包括三部分：由于条纹投射测量系统设置引起的载波相位，以及分别由投影仪和相机的镜头畸变误差引起的相位误差。由于相机标定方法非常成熟，且精度高。因此，根据相机标定结果对采集的条纹图预处理——即去畸变校正，即可消除相机镜头畸变对测量相位的影响。投影仪的镜头畸变量通常都很小，很难直接通过裸眼观察发现投射的条纹图变形。在这种情 况下，利用公式
Figure PCTCN2016097664-appb-000006
拟合测量的绝对相位，可获得载波相位分布。最后将测量的绝对相位减去拟合的载波相位，可获得由于投影仪的镜头畸变引起的相位误差ΔΦa，其中，ΔΦa＝Φm-Φc。显然，这样容易获得在投射水平和竖直相移条纹后，由于投影仪的镜头畸变引起的相位误差(ΔΦa，h，ΔΦa，v)。
在步骤S3中，步骤三、定义垂直于投影仪镜头光轴的一平面G，根据所述相位误差计算平面G与投影平面的映射关系。
在本实施方式中，所述步骤三具体包括：
利用步骤一中测量的绝对相位(Φm，h，Φm，v)，建立投影平面与相机像面之间等相位点对的映射关系为
Figure PCTCN2016097664-appb-000007
其中，(s1，t1)为投影平面上的像素点，(s1，t1)像素点的相位与相机像面上的像素点(i，j)的相位相等；
根据步骤二中得到的相位误差(ΔΦa，h，ΔΦa，v)建立三维数据点集(s1，t1，ΔΦa，h(i，j))和(s1，t1，ΔΦa，v(i，j))；
利用泽尼克多项式(Zernike Polynomials)拟合上述两个三维数据点集(s1，t1，ΔΦa，h(i，j))和(s1，t1，ΔΦa，v(i，j))，根据拟合的系数计算投影平面上整数像素点(s，t)的相位误差(ΔΦa，h(s，t)，ΔΦa，v(s，t))；
通过公式
Figure PCTCN2016097664-appb-000008
建立平面G和投影平面之间的映射关系，其中，(s2，t2)为平面G在投影平面上的映射点。
在步骤S4中，根据所述映射关系，生成变频、相移自适应条纹用于投影，使得投影仪投出的条纹在平面G上为标准的正弦条纹。
在本实施方式中，所述步骤四具体包括：
定义期望在平面G上获得的条纹图的相位分布；
根据步骤三中建立的映射关系以及平面G上的相位分布，计算投影平面上整数像素点的相位
Figure PCTCN2016097664-appb-000009
利用公式
Figure PCTCN2016097664-appb-000010
生成自适应条纹图，其中，
Figure PCTCN2016097664-appb-000011
表示自适应条纹图在像素点(s，t)处的强度，Imax表示自适应条纹图的最大强度。
本发明提供的一种基于自适应条纹的投影仪镜头畸变校正方法，首先获取标准平板的绝对相位，然后利用绝对相位计算由于投影仪的镜头畸变引起的相位误差，接着定义垂直于投影仪光轴的某一平面G，利用相位误差建立平面G与投影平面之间的映射关系，最后根据建立的映射关系，生成自适应条纹图用于投影，即可投影仪镜头畸变对条纹图的影响，在平面G上获得标准的正弦条纹图。这种方法无需标定投影仪和测量系统参数，如投影仪的镜头畸变系数、投影仪和相机光轴之间的夹角等，能够降低计算复杂度、改善测量结果的精度，适用于任意设置的条纹投射测量系统。
以下将对本发明所提供的一种基于自适应条纹的投影仪镜头畸变校正系统进行详细说明。
请参阅图2，所示为本发明一实施方式中基于自适应条纹的投影仪镜头畸变校正系统10的结构示意图。
在本实施方式中，基于自适应条纹的投影仪镜头畸变校正系统10，主要包括相位获取模块11、误差计算模块12、映射计算模块13以及条纹生成模块14。
相位获取模块11，用于利用条纹投影测量系统获取标准平板的绝对相位。
在本实施方式中，所述相位获取模块11具体用于：
利用投影仪向标准平板分别投射一套竖直和水平的变频、相移正弦条纹图，然后采用条纹分析技术分析相机记录的正弦条纹图，并获得标准平板的绝对相 位(Φm，h，Φm，v)。
在本实施方式中，将标准平板任意放置在条纹投射系统的测量空间内，利用投影仪向平板分别投射一套变频、相移的水平和竖直正弦条纹图。假设利用相机记录的第k帧条纹图强度
Figure PCTCN2016097664-appb-000012
可表示为
Figure PCTCN2016097664-appb-000013
其中，I′(i，j)表示平均强度，I″(i，j)表示调制度，Φ(i，j)表示待求的相位，δk＝2πN/k表示相邻两帧条纹图之间的相移量，N表示相移次数。根据相移算法，包裹相位Φw可由下式计算求得：
Figure PCTCN2016097664-appb-000014
其中，利用相位解包裹算法对Φw展开，可获得待测平板的两个绝对相位Φm，h和Φm，v。
误差计算模块12，用于根据所述绝对相位，计算由于投影仪的镜头畸变引起的相位误差。
在本实施方式中，所述误差计算模块12具体用于：
利用公式
Figure PCTCN2016097664-appb-000015
拟合测量的绝对相位获得载波相位分布，其中，Φc(i，j)表示在像素点(i，j)处拟合的载波相位，r，s，t，u，v表示与系统参数相关的系数；
然后将测量的绝对相位(Φm，h，Φm，v)减去拟合的载波相位Φc(i，j)，即可获得由于投影仪的镜头畸变引起的相位误差(ΔΦa，h，ΔΦa，v)。
在本实施方式中，假设忽略投影仪和相机的镜头畸变影响，则平板的绝对 相位可用如下公式表示
Figure PCTCN2016097664-appb-000016
Φc(i，j)表示在像素点(i，j)处拟合的载波相位，r，s，t，u，v表示与系统参数相关的系数。然而，对于实际的条纹投射系统，投影仪和相机的镜头畸变对测量结果的影响不可忽略，标准平板绝对相位的测量结果包括三部分：由于条纹投射测量系统设置引起的载波相位，以及分别由投影仪和相机的镜头畸变误差引起的相位误差。由于相机标定方法非常成熟，且精度高。因此，根据相机标定结果对采集的条纹图预处理——即去畸变校正，即可消除相机镜头畸变对测量相位的影响。投影仪的镜头畸变量通常都很小，很难直接通过裸眼观察发现投射的条纹图变形。在这种情况下，利用公式
Figure PCTCN2016097664-appb-000017
拟合测量的绝对相位，可获得载波相位分布。最后将测量的绝对相位减去拟合的载波相位，可获得由于投影仪的镜头畸变引起的相位误差ΔΦa，其中，ΔΦa＝Φm-Φc。显然，这样容易获得在投射水平和竖直相移条纹后，由于投影仪的镜头畸变引起的相位误差(ΔΦa，h，ΔΦa，v)。
映射计算模块13，用于定义垂直于投影仪镜头光轴的一平面G，根据所述相位误差计算平面G与投影平面的映射关系。
在本实施方式中，所述映射计算模块13具体用于：
利用所述绝对相位(Φm，h，Φm，v)，建立投影平面与相机像面之间等相位点对的映射关系为
Figure PCTCN2016097664-appb-000018
其中，(s1，t1)为投影平面上的像素点，(s1，t1)像素点的相位与相机像面上的像素点(i，j)的相位相等；
根据得到的相位误差(ΔΦa，h，ΔΦa，v)建立三维数据点集(s1，t1，ΔΦa，h(i，j))和(s1，t1，ΔΦa，v(i，j))；
利用泽尼克多项式拟合上述两个三维数据点集(s1，t1，ΔΦa，h(i，j))和(s1，t1，ΔΦa，v(i，j))，根据拟合的系数计算投影平面上整数像素点(s，t)的相位误差(ΔΦa，h(s，t)，ΔΦa，v(s，t))；
通过公式
Figure PCTCN2016097664-appb-000019
建立平面G和投影平面之间的映射关系，其中，(s2，t2)为平面G在投影平面上的映射点。
条纹生成模块14，用于根据所述映射关系，生成变频、相移自适应条纹用于投影，使得投影仪投出的条纹在平面G上为标准的正弦条纹。
在本实施方式中，所述条纹生成模块14具体用于：
定义期望在平面G上获得的条纹图的相位分布；
根据建立的映射关系以及平面G上的相位分布，计算投影平面上整数像素点的相位
Figure PCTCN2016097664-appb-000020
利用公式
Figure PCTCN2016097664-appb-000021
生成自适应条纹图，其中，
Figure PCTCN2016097664-appb-000022
表示自适应条纹图在像素点(s，t)处的强度，Imax表示自适应条纹图的最大强度。
本发明提供的一种基于自适应条纹的投影仪镜头畸变校正系统10，无需标定投影仪和测量系统参数，如投影仪的镜头畸变系数、投影仪和相机光轴之间的夹角等，能够降低计算复杂度、改善测量结果的精度，适用于任意设置的条纹投射测量系统。
为了测试基于自适应条纹的投影仪镜头畸变误差校正方法的有效性，对一陶瓷板(平面度小于0.01mm)测量。首先利用本发明所提方法生成一套变频(条纹宽度分别为13，14，15个像素)、相移(四步相移)自适应条纹，然后将其依次投射到标准平板上，并通过相机记录条纹图，采用条纹分析技术处理条纹图像。图3(a)为实际测量相位减去载波相位后的残差分布，图3(b)为重建的平板 三维数据。为了计算重建结果的精度，采用最小二乘拟合算法拟合平板的测量结果，图3(c)为测量三维数据与拟合结果的偏差分布。同时，为了与常规条纹投射测量方法比较，利用计算机生成一套标准的相移正弦条纹图，并投射到陶瓷平板上测量。图3(d)为投射标准正弦相移条纹图后恢复的相位误差。从图中可知，投影仪的镜头畸变会导致投射的条纹图变形，使得相位恢复结果中存在误差，影响三维重建结果的精度，而采用本发明所提方法能够有效抑制投影仪镜头畸变对条纹图的影响，获得准确的三维重建结果。
此外，为了检验本发明方法的重复性和精度，将陶瓷板任意摆放在11处不同的位置，在每个位置处，利用本发明所提方法向陶瓷板投射自适应条纹图，并重建三维测量结果，最后利用最小二乘拟合算法计算测量数据与拟合结果之间的偏差。表1统计了11处测量结果的偏差的PV(Peak to valley)值和RMS(Root-mean-square)值。
表1.陶瓷平面11次测量的统计结果
Figure PCTCN2016097664-appb-000023
从表中可知，本发明所提方法能够在系统测量空间内获得稳定的测量结果。同时，为了检验本发明所提方法的精度，将陶瓷平板安装在高精度的移动导轨(分辨率为1.25μm)，通过该导轨将陶瓷板分别移动在不同的位置。在每个位置处，采用本发明所提方法向陶瓷板投射自适应条纹图，并重建三维测量结果。图4为陶瓷平板中心区域某一截线轮廓的测量结果。从图中可知，利用本发明所提方法的重建误差为±0.1mm。
最后，为了与现有投影仪标定方法比较，采用相位辅助法标定投影仪。图5为投影仪和相机标定结果的重投影误差，从图中可知，投影仪标定结果的重投影误差比相机标定结果的重投影误差大，这一结果证明投影仪标定方法的精 度明显低于相机的标定精度。利用上述标定结果对同一陶瓷平板测量，并采用文献中所述方法重建三维数据，图6为重建三维数据与最小二乘拟合结果的偏差分布，从图中可知重建结果误差的PV和RMS值分别为0.378mm和0.035mm。此外，图中边缘区域的重建误差明显大于中心区域，这主要是因为投影仪的标定结果存在一定的误差，假设实际像点与像面中心点的距离为d，当采用非线性畸变模型计算与实际像点对应的理想像点时，计算误差随着d的增大而增加，最终导致边缘重建结果的精度明显低于中心区域。上述测量结果间接证明了本发明所提方法能够有效抑制投影仪的镜头畸变误差，提高三维重建结果的精度。
值得注意的是，上述实施例中，所包括的各个单元只是按照功能逻辑进行划分的，但并不局限于上述的划分，只要能够实现相应的功能即可；另外，各功能单元的具体名称也只是为了便于相互区分，并不用于限制本发明的保护范围。
另外，本领域普通技术人员可以理解实现上述各实施例方法中的全部或部分步骤是可以通过程序来指令相关的硬件来完成，相应的程序可以存储于一计算机可读取存储介质中，所述的存储介质，如ROM/RAM、磁盘或光盘等。
以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。

Claims (10)

  1. 一种基于自适应条纹的投影仪镜头畸变校正方法，其特征在于，所述方法包括：
    步骤一、利用条纹投影测量系统获取标准平板的绝对相位；
    步骤二、根据所述绝对相位，计算由于投影仪的镜头畸变引起的相位误差；
    步骤三、定义垂直于投影仪镜头光轴的一平面G，根据所述相位误差计算平面G与投影平面的映射关系；
    步骤四、根据所述映射关系，生成变频、相移自适应条纹用于投影，使得投影仪投出的条纹在平面G上为标准的正弦条纹。
  2. 如权利要求1所述的基于自适应条纹的投影仪镜头畸变校正方法，其特征在于，所述步骤一具体包括：
    利用投影仪向标准平板分别投射一套竖直和水平的变频、相移正弦条纹图，然后采用条纹分析技术分析相机记录的正弦条纹图，并获得标准平板的绝对相位(Φm，h，Φm，v)。
  3. 如权利要求2所述的基于自适应条纹的投影仪镜头畸变校正方法，其特征在于，所述步骤二具体包括：
    利用公式
    Figure PCTCN2016097664-appb-100001
    拟合测量的绝对相位获得载波相位分布，其中，Φc(i，j)表示在像素点(i，j)处拟合的载波相位，r，s，t，u，v表示与系统参数相关的系数；
    然后将测量的绝对相位(Φm，h，Φm，y)减去拟合的载波相位Φc(i，j)，即可获得由于投影仪的镜头畸变引起的相位误差(ΔΦa，h，ΔΦa，v)。
  4. 如权利要求3所述的基于自适应条纹的投影仪镜头畸变校正方法，其特征在于，所述步骤三具体包括：
    利用步骤一中测量的绝对相位(Φm，h，Φm，v)，建立投影平面与相机像面之间 等相位点对的映射关系为
    Figure PCTCN2016097664-appb-100002
    其中，(s1，t1)为投影平面上的像素点，(s1，t1)像素点的相位与相机像面上的像素点(i，j)的相位相等；
    根据步骤二中得到的相位误差(ΔΦa，h，ΔΦa，v)建立三维数据点集(s1，t1，ΔΦa，h(i，j))和(s1，t1，ΔΦa，v(i，j))；
    利用泽尼克多项式拟合上述两个三维数据点集(s1，t1，ΔΦa，h(i，j))和(s1，t1，ΔΦa，v(i，j))，根据拟合的系数计算投影平面上整数像素点(s，t)的相位误差(ΔΦa，h(s，t)，ΔΦa，v(s，t))；
    通过公式
    Figure PCTCN2016097664-appb-100003
    建立平面G和投影平面之间的映射关系，其中，(s2，t2)为平面G在投影平面上的映射点。
  5. 如权利要求4所述的基于自适应条纹的投影仪镜头畸变校正方法，其特征在于，所述步骤四具体包括：
    定义期望在平面G上获得的条纹图的相位分布；
    根据步骤三中建立的映射关系以及平面G上的相位分布，计算投影平面上整数像素点的相位
    Figure PCTCN2016097664-appb-100004
    利用公式
    Figure PCTCN2016097664-appb-100005
    生成自适应条纹图，其中，
    Figure PCTCN2016097664-appb-100006
    表示自适应条纹图在像素点(s，t)处的强度，Imax表示自适应条纹图的最大强度。
  6. 一种基于自适应条纹的投影仪镜头畸变校正系统，其特征在于，所述系统包括：
    相位获取模块，用于利用条纹投影测量系统获取标准平板的绝对相位；
    误差计算模块，用于根据所述绝对相位，计算由于投影仪的镜头畸变引起 的相位误差；
    映射计算模块，用于定义垂直于投影仪镜头光轴的一平面G，根据所述相位误差计算平面G与投影平面的映射关系；
    条纹生成模块，用于根据所述映射关系，生成变频、相移自适应条纹用于投影，使得投影仪投出的条纹在平面G上为标准的正弦条纹。
  7. 如权利要求6所述的基于自适应条纹的投影仪镜头畸变校正系统，其特征在于，所述相位获取模块具体用于：
    利用投影仪向标准平板分别投射一套竖直和水平的变频、相移正弦条纹图，然后采用条纹分析技术分析相机记录的正弦条纹图，并获得标准平板的绝对相位(Φm，h，Φm，v)。
  8. 如权利要求7所述的基于自适应条纹的投影仪镜头畸变校正系统，其特征在于，所述误差计算模块具体用于：
    利用公式
    Figure PCTCN2016097664-appb-100007
    拟合测量的绝对相位获得载波相位分布，其中，Φc(i，j)表示在像素点(i，j)处拟合的载波相位，r，s，t，u，v表示与系统参数相关的系数；
    然后将测量的绝对相位(Φm，h，Φm，v)减去拟合的载波相位Φc(i，j)，即可获得由于投影仪的镜头畸变引起的相位误差(ΔΦa，h，ΔΦa，v)。
  9. 如权利要求8所述的基于自适应条纹的投影仪镜头畸变校正系统，其特征在于，所述映射计算模块具体用于：
    利用所述绝对相位(Φm，h，Φm，v)，建立投影平面与相机像面之间等相位点对的映射关系为
    Figure PCTCN2016097664-appb-100008
    其中，(s1，t1)为投影平面上的像素点，(s1，t1)像素点的相位与相机像面上的像素点(i，j)的相位相等；
    根据得到的相位误差(ΔΦa，h，ΔΦa，v)建立三维数据点集(s1，t1，ΔΦa，h(i，j))和(s1，t1，ΔΦa，v(i，j))；
    利用泽尼克多项式拟合上述两个三维数据点集(s1，t1，ΔΦa，h(i，j))和(s1，t1，ΔΦa，v(i，j))，根据拟合的系数计算投影平面上整数像素点(s，t)的相位误差(ΔΦa，h(s，t)，ΔΦa，v(s，t))；
    通过公式
    Figure PCTCN2016097664-appb-100009
    建立平面G和投影平面之间的映射关系，其中，(s2，t2)为平面G在投影平面上的映射点。
  10. 如权利要求9所述的基于自适应条纹的投影仪镜头畸变校正系统，其特征在于，所述条纹生成模块具体用于：
    定义期望在平面G上获得的条纹图的相位分布；
    根据建立的映射关系以及平面G上的相位分布，计算投影平面上整数像素点的相位
    Figure PCTCN2016097664-appb-100010
    利用公式
    Figure PCTCN2016097664-appb-100011
    生成自适应条纹图，其中，
    Figure PCTCN2016097664-appb-100012
    表示自适应条纹图在像素点(s，t)处的强度，Imax表示自适应条纹图的最大强度。
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