CN107610183A - New striped projected phase height conversion mapping model and its scaling method - Google Patents

New striped projected phase height conversion mapping model and its scaling method Download PDF

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CN107610183A
CN107610183A CN201710874303.XA CN201710874303A CN107610183A CN 107610183 A CN107610183 A CN 107610183A CN 201710874303 A CN201710874303 A CN 201710874303A CN 107610183 A CN107610183 A CN 107610183A
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孙长库
陆鹏
王鹏
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Tianjin University
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Abstract

本发明公开了一种新型条纹投影相位高度转换映射模型及标定方法:标定靶标放在相机视场和投射器投影区域交界处区域内,拍摄标定靶标图像,发射投射条纹,同时拍摄图像;标定靶标放置在另一位置,标定靶标与之前姿态不同,重复上述;采集足够图像;提取特征点图像坐标信息,利用插值法计算对应特征点绝对相位值,标定相机;所有特征点坐标值转换到CCS下,利用特征点的信息,计算出相位高度转换映射模型中的各个参数。本发明解决了标定技术中存在的适用性不强,对相机和投射器相对位姿有严格要求,模型算法复杂度高,标定过程复杂以及存在误差累积等的问题。

The invention discloses a novel fringe projection phase-height conversion mapping model and calibration method: The calibration target is placed in the junction of the camera field of view and the projection area of the projector, and the calibration target image is taken, the projection stripe is emitted, and the image is taken at the same time; the calibration target is placed in another position, and the calibration target is different from the previous posture, repeat the above; the collection is enough Image; extract the image coordinate information of feature points, use interpolation to calculate the absolute phase value of the corresponding feature point, and calibrate the camera; convert all the coordinate values of the feature points to CCS, and use the information of the feature points to calculate each parameter in the phase-height conversion mapping model . The invention solves the problems of poor applicability in the calibration technology, strict requirements on the relative poses of the camera and the projector, high complexity of the model algorithm, complex calibration process and error accumulation.

Description

新型条纹投影相位高度转换映射模型及其标定方法A new fringe projection phase-height conversion mapping model and its calibration method

技术领域technical field

本发明涉及光学三维检测技术,更具体的说,是涉及一种新型条纹投影相位高度转换映射模型及其标定方法。The invention relates to optical three-dimensional detection technology, more specifically, relates to a novel fringe projection phase-height conversion mapping model and a calibration method thereof.

背景技术Background technique

系统标定技术对于条纹投影三维测量系统的准确度、速度和系统组成有很大的影响,现存的标定技术可以分为两种:基于立体视觉的标定技术和相位高度转换技术。System calibration technology has a great influence on the accuracy, speed and system composition of fringe projection three-dimensional measurement system. Existing calibration technology can be divided into two types: calibration technology based on stereo vision and phase-height conversion technology.

受双目视觉系统启发,许多研究人员研究并改进了基于立体视觉的标定技术。为了实现三维测量,标定时投射器和相机的内部参数以及二者之间的旋转矩阵、平移向量均需要被标定计算出来。Zhang和Huang提出了一种标定方法,其中投射器可以像相机一样“拍摄”图像。这种方法通过投射一系列的水平和竖直条纹来标定投射器并建立投射器和相机的空间关系。Li等人利用预畸变投射条纹的方法消除了投射器镜头畸变造成的影响。为了进一步提高测量准确度,Li和Zhang提出了一种算法估计投射器的最佳投射角。最近,Chen等人提出一种自标定方法实现了条纹投影测量系统的在线标定。由于需要投射各种图案以标定投射器并计算投射器和相机的空间关系,基于立体视觉的标定技术仅适用于投射器是液晶显示器(LCD)或者数字微透镜阵列(DMD)的情况。然而,在某些情况下,比如莫尔条纹投影系统,光纤干涉投影系统和扫描频闪条纹投影系统,这种技术不再适用,因为这些系统中的投射器不能被看作“反向”的相机。Inspired by the binocular vision system, many researchers have studied and improved stereo vision-based calibration techniques. In order to realize three-dimensional measurement, the internal parameters of the projector and the camera, as well as the rotation matrix and translation vector between the two need to be calibrated and calculated. Zhang and Huang proposed a calibration method in which a projector "shoots" an image like a camera. This method calibrates the projector and establishes the spatial relationship between the projector and the camera by projecting a series of horizontal and vertical stripes. Li et al. used the method of pre-distorting projected fringes to eliminate the influence of projector lens distortion. To further improve the measurement accuracy, Li and Zhang proposed an algorithm to estimate the optimal projection angle of the projector. Recently, Chen et al. proposed a self-calibration method to realize the online calibration of the fringe projection measurement system. Due to the need to project various patterns to calibrate the projector and calculate the spatial relationship between the projector and the camera, stereo vision-based calibration techniques are only applicable when the projector is a liquid crystal display (LCD) or a digital microlens array (DMD). However, in some cases, such as moiré fringe projection systems, fiber optic interference projection systems and scanning strobe fringe projection systems, this technique is no longer applicable because the projectors in these systems cannot be seen as "reverse" camera.

另一个分支是相位高度转换标定技术。这种模型不考虑标定投射器,而是通过数学模型直接建立相位和高度的关系。因此,不受投射器种类的约束。受插值法的启发,Léandry等人提出了一种多项式映射的模型来建立相位和高度映射关系。为了达到较高的测量准确度,多项式的次数需要不小于4,因此测量过程费时,不适合用于实时测量系统中。Lu等人提出了一种基于条纹几何约束的相位高度转换方法。这种方法具有高测量准确度和强鲁棒性,但是同样存在计算量大的缺点。Du等人利用相机针孔模型结合光线追迹理论建立了相位和高度的映射关系,Huang通过考虑相机镜头的畸变提高了这种模型的准确度。对应的标定方法需要不同高度的量块和参考面,因此限制了它们的应用范围。此外,文献中模型参数有34个,计算量大。Tavares等人利用实验经验提出了相位差和高度的映射关系。Zhang等人通过多项式映射的方法建立世界坐标和相位差的一对一映射公式。文献中的方法本质上是利用查找表法(LUT)的像素级标定方法。这些方法依赖于相位图中每个像素精确的相位值,因此需要标定板移动足够的位置,标定过程费时。另外,这两种模型都需要参考平面来计算相位差,会产生误差累积的问题。Another branch is phase-height conversion calibration technology. This model does not consider the calibration of the projector, but directly establishes the relationship between phase and height through a mathematical model. Therefore, it is not bound by the type of caster. Inspired by the interpolation method, Léandry et al. proposed a polynomial mapping model to establish the phase and height mapping relationship. In order to achieve high measurement accuracy, the degree of the polynomial needs to be not less than 4, so the measurement process is time-consuming and not suitable for real-time measurement systems. Lu et al. proposed a phase-height conversion method based on fringe geometric constraints. This method has high measurement accuracy and strong robustness, but also has the disadvantage of large amount of calculation. Du et al. used the camera pinhole model combined with ray tracing theory to establish the mapping relationship between phase and height. Huang improved the accuracy of this model by considering the distortion of the camera lens. The corresponding calibration methods require gauge blocks and reference surfaces of different heights, thus limiting their range of application. In addition, there are 34 model parameters in the literature, which is computationally intensive. Tavares et al proposed a mapping relationship between phase difference and height by using experimental experience. Zhang et al. established a one-to-one mapping formula between world coordinates and phase difference by means of polynomial mapping. The methods in the literature are essentially pixel-level calibration methods using look-up tables (LUTs). These methods rely on the precise phase value of each pixel in the phase map, so the calibration plate needs to be moved enough, and the calibration process is time-consuming. In addition, both models need a reference plane to calculate the phase difference, which will cause the problem of error accumulation.

发明内容Contents of the invention

本发明的目的是为了克服现有技术中的不足,通过建立虚拟相机坐标系以及分析条纹信息在相机坐标系和投射器坐标系之间的转换关系,提供了一种针对条纹投影三维测量系统的改进的相位高度转换映射模型及标定方法,解决了上述标定技术中存在的适用性不强,对相机和投射器相对位姿有严格要求,模型算法复杂度高,标定过程复杂以及存在误差累积等的问题。The purpose of the present invention is to overcome the deficiencies in the prior art, by establishing a virtual camera coordinate system and analyzing the conversion relationship between the camera coordinate system and the projector coordinate system of the fringe information, providing a three-dimensional measurement system for fringe projection The improved phase-height conversion mapping model and calibration method solve the problems of poor applicability in the above-mentioned calibration technology, strict requirements on the relative pose of the camera and the projector, high complexity of the model algorithm, complex calibration process, and error accumulation, etc. The problem.

本发明的目的可通过以下技术方案实现。The purpose of the present invention can be achieved through the following technical solutions.

一种新型条纹投影相位高度转换映射模型,相位高度转换映射模型为:A new fringe projection phase-height conversion mapping model, the phase-height conversion mapping model is:

其中,in,

kij=b3pij+b4qij k ij =b 3 p ij +b 4 q ij

[u v]T代表未经畸变校正的图像坐标;[u" v"]T是变换后的图像坐标;投射器坐标系PCS中圆点OP代表发光点,XP轴平行于投射条纹相位变化的方向,YP轴垂直投射条纹相位变化的方向,ZP轴垂直于投射条纹的相平面,在投射器坐标系PCS中任意一点的坐标表示为[XP YP ZP]T,在投射器坐标系PCS中,同一条光线上的空间点相位相同,均为φ,在同一高度ZP上,相位值从φ0变化到φ1,对应的XP变化范围是[XP0),XP1)];w是尺度因子;TP是平移向量,TP=[tX tY tZ]T;[fu fv]T代表镜头的焦距,[uo vo]T是图像中心坐标;s是图像坐标轴的扭曲系数。[uv] T represents the image coordinates without distortion correction; [u"v"] T is the transformed image coordinates ; the dot OP in the projector coordinate system PCS represents the luminous point, and the X P axis is parallel to the projected fringe phase change The direction of the Y P axis is perpendicular to the direction of the phase change of the projected fringe, and the Z P axis is perpendicular to the phase plane of the projected fringe. The coordinates of any point in the projector coordinate system PCS are expressed as [X P Y P Z P ] T , in the projected In the sensor coordinate system PCS, the phases of the spatial points on the same ray are the same, φ, and at the same height Z P , the phase value changes from φ 0 to φ 1 , and the corresponding X P variation range is [X P0 ),X P1 )]; w is the scale factor; T P is the translation vector, T P =[t X t Y t Z ] T ; [fu f v ] T represents the focal length of the lens, [ u o v o ] T is the center coordinate of the image; s is the distortion coefficient of the image coordinate axis.

为了降低算法复杂度,实现实时测量,利用查找表LUT法,定义In order to reduce the complexity of the algorithm and realize real-time measurement, the look-up table LUT method is used to define

则高度转换映射模型Zc简化为:Then the height conversion mapping model Zc is simplified as:

本发明的目的可通过以下技术方案实现。The purpose of the present invention can be achieved through the following technical solutions.

一种新型条纹投影相位高度转换映射模型的标定方法,包括以下步骤:A calibration method for a novel fringe projection phase-height conversion mapping model, comprising the following steps:

步骤一,将标定靶标放在相机视场和投射器投影区域交界处的区域内,相机拍摄标定靶标图像,然后投射器发射投射条纹,同时相机拍摄图像;Step 1, place the calibration target in the area at the junction of the camera field of view and the projection area of the projector, the camera captures the image of the calibration target, then the projector emits projection stripes, and the camera captures images at the same time;

步骤二,将标定靶标放置在相机视场和投射器投影区域交界处区域内另一位置,且标定靶标与之前的姿态不同,重复步骤一;Step 2, place the calibration target at another position in the junction of the camera field of view and the projection area of the projector, and the calibration target is different from the previous posture, repeat step 1;

步骤三,重复步骤二直至采集到足够图像,一般是2~10组图像;Step 3, repeat step 2 until enough images are collected, usually 2 to 10 groups of images;

步骤四,提取特征点的图像坐标信息,并利用插值法计算对应特征点的绝对相位值,标定相机;Step 4, extract the image coordinate information of the feature points, and use the interpolation method to calculate the absolute phase value of the corresponding feature points, and calibrate the camera;

步骤五,将所有特征点的坐标值转换到相机坐标系CCS下,利用特征点的信息(ZC;u v φ),计算出本发明新型条纹投影相位高度转换映射模型中的各个参数。Step 5: Convert the coordinate values of all feature points to the camera coordinate system CCS, and use the information (Z C ; uv φ) of the feature points to calculate each parameter in the new fringe projection phase-height conversion mapping model of the present invention.

与现有技术相比,本发明的技术方案所带来的有益效果是:Compared with the prior art, the beneficial effects brought by the technical solution of the present invention are:

本发明针对条纹投影测量系统,通过建立虚拟的相机坐标系以及分析投射条纹信息在投射器坐标系和相机坐标系之间的转换关系,提出了一种改进的相位高度映射模型,并且针对这种模型提出了一种新颖的标定方法。相比于之前针对条纹投影测量系统的映射模型和标定方法,本文提出的模型不仅对投射器和相机的相对位姿无严格要求,标定模型算法复杂度低,能够实现快速准确的三维测量,而且对应的标定方法简单高效。由于本发明提出的相位高度映射模型以及标定方法具有以上优点,因此可以应用于现场标定。Aiming at the fringe projection measurement system, the present invention proposes an improved phase-height mapping model by establishing a virtual camera coordinate system and analyzing the conversion relationship between the projected fringe information between the projector coordinate system and the camera coordinate system. The model proposes a novel calibration method. Compared with the previous mapping model and calibration method for the fringe projection measurement system, the model proposed in this paper not only does not have strict requirements on the relative pose of the projector and the camera, but the calibration model algorithm has low complexity and can achieve fast and accurate 3D measurement. The corresponding calibration method is simple and efficient. Since the phase-height mapping model and the calibration method proposed by the present invention have the above advantages, they can be applied to field calibration.

附图说明Description of drawings

图1是投射器坐标系PCS示意图;Figure 1 is a schematic diagram of the projector coordinate system PCS;

图2是虚拟相机坐标系CCS'和相机坐标系CCS示意图;Fig. 2 is a schematic diagram of the virtual camera coordinate system CCS' and the camera coordinate system CCS;

图3是条纹投影相位高度转换映射模型的标定原理图;Figure 3 is a schematic diagram of the calibration of the fringe projection phase-height conversion mapping model;

图4是利用条纹投影相位高度转换映射模型的标定现场图;Fig. 4 is a calibration site map using the fringe projection phase-height conversion mapping model;

图5是利用本模型测量的被测物示意图;Fig. 5 is a schematic diagram of the measured object measured by this model;

图6是标定所用特征点重建信息示意图;Fig. 6 is a schematic diagram of reconstruction information of feature points used for calibration;

图7是利用本模型进行三维测量的结果示意图。Figure 7 is a schematic diagram of the results of three-dimensional measurement using this model.

具体实施方式detailed description

下面结合附图对本发明作进一步的描述。The present invention will be further described below in conjunction with the accompanying drawings.

如图1所示,建立一个投射器坐标系PCS,其中圆点OP代表发光点,XP轴平行于投射条纹相位变化的方向,YP轴垂直投射条纹相位变化的方向,ZP轴垂直于投射条纹的相平面。因此,在投射器坐标系PCS中任意一点的坐标可以表示为[XP YP ZP]T。由图1可知,在投射器坐标系PCS中,同一条光线上的空间点相位相同,均为φ。在同一高度ZP上,相位值从φ0变化到φ1,对应的XP变化范围是[XP0),XP1)]。对于从OP发出的任意光线,可以获得式(1):As shown in Figure 1, a projector coordinate system PCS is established, where the dot OP represents the luminous point, the X P axis is parallel to the direction of the phase change of the projected fringe, the Y P axis is perpendicular to the direction of the projected fringe phase change, and the Z P axis is vertical on the phase plane of the projected fringes. Therefore, the coordinates of any point in the projector coordinate system PCS can be expressed as [X P Y P Z P ] T . It can be seen from Fig. 1 that in the projector coordinate system PCS, the phases of the spatial points on the same ray are the same, all of which are φ. At the same height Z P , the phase value changes from φ 0 to φ 1 , and the corresponding change range of XP is [X P0 ),X P ( φ 1 )]. For any ray emitted from OP , equation (1) can be obtained:

XP=wZP(φ-φ0)+XP0) (1)X P =wZ P (φ-φ 0 )+X P0 ) (1)

其中,w是尺度因子。相机坐标系CCS到投射器坐标系PCS的坐标变换公式为:where w is the scaling factor. The coordinate transformation formula from the camera coordinate system CCS to the projector coordinate system PCS is:

[XP YP ZP]T=TP+RP[XC YC ZC]T (2)[X P Y P Z P ] T =T P +R P [X C Y C Z C ] T (2)

其中,RP是旋转矩阵,TP是平移向量,[XC YC ZC]T是相机坐标系中的坐标,Among them, R P is the rotation matrix, T P is the translation vector, [X C Y C Z C ] T is the coordinates in the camera coordinate system,

TP=[tX tY tZ]T T P =[t X t Y t Z ] T

这里,定义一个虚拟相机坐标系CCS',使其同投射器坐标系PCS具有相同的姿态,同相机坐标系CCS具有相同的位置,如图2和式(3)所示。Here, a virtual camera coordinate system CCS' is defined so that it has the same posture as the projector coordinate system PCS and the same position as the camera coordinate system CCS, as shown in Figure 2 and formula (3).

[XP YP ZP]T=TP+[XC' YC' ZC']T (3)[X P Y P Z P ] T =T P +[X C' Y C' Z C' ] T (3)

其中,[XC' YC' ZC']T=RP[XC YC ZC]TWherein, [X C' Y C' Z C' ] T = R P [X C Y C Z C ] T .

将式(3)带入式(1),可得式(4):Putting formula (3) into formula (1), we can get formula (4):

XC'+tX=w(ZC'+tZ)(φ-φ0)+XP0) (4)X C' +t X =w(Z C' +t Z )(φ-φ 0 )+X P0 ) (4)

将相机小孔成像模型带入式(4),可得式(5):Putting the camera pinhole imaging model into Equation (4), Equation (5) can be obtained:

其中, in,

上式中[XC' YC' ZC']T表示相机坐标系CCS'中的坐标;[fu fv]T代表镜头的焦距,[uovo]T是图像中心坐标;s是图像坐标轴的扭曲系数。展开式(3)并且令XC'和YC'分别除以ZC',并利用相机成像模型,可得式(6):In the above formula, [X C' Y C' Z C' ] T represents the coordinates in the camera coordinate system CCS'; [f u f v ] T represents the focal length of the lens, [u o v o ] T is the image center coordinates; s is the distortion factor for the image coordinate axes. Expand equation (3) and divide X C' and Y C' by Z C ' respectively, and use the camera imaging model to obtain equation (6):

其中, in,

利用泰勒级数将式(6)展开,结果如式(7),Using Taylor series to expand formula (6), the result is as formula (7),

对相机镜头的畸变进行校正,相机镜头畸变模型如式(8),The distortion of the camera lens is corrected, and the camera lens distortion model is shown in formula (8),

其中,[u v]T代表未经畸变校正的图像坐标,[uun vun]T代表校正后的图像坐标;e1,e2和e3代表径向畸变参数,g1和g2代表切向畸变参数,表示图像坐标点和中心点的距离。为了避免寻找图像中心坐标[uo vo]T,展开式(8)。同时,展开式(7)。式(7)和式(8)展开后的结果均可以用式(9)表示,其中[u" v"]T是变换后的图像坐标,Among them, [uv] T represents the image coordinates without distortion correction, [u un v un ] T represents the corrected image coordinates; e 1 , e 2 and e 3 represent the radial distortion parameters, g 1 and g 2 represent the cut to the distortion parameter, Indicates the distance between the image coordinate point and the center point. In order to avoid searching for the image center coordinate [u o v o ] T , expand (8). At the same time, expand formula (7). The expanded results of Equation (7) and Equation (8) can be expressed by Equation (9), where [u"v"] T is the transformed image coordinate,

在相机坐标系CCS中考虑到相机镜头的畸变,将式(9)带入式(5)中,得到本发明的新型条纹投影相位高度转换映射模型ZC(u,v,φ),可以表示为:Considering the distortion of the camera lens in the camera coordinate system CCS, formula (9) is brought into formula (5), and the novel fringe projection phase-height conversion mapping model Z C (u, v, φ) of the present invention is obtained, which can be expressed as for:

其中,kij=b3pij+b4qij。式(10)可以认为是CCS中的图像坐标进行相机镜头畸变校正后转换到CCS'中的图像坐标的情况。Among them, k ij =b 3 p ij +b 4 q ij . Equation (10) can be considered as the case where the image coordinates in CCS are converted to image coordinates in CCS' after correction of camera lens distortion.

式(10)中的参数可以通过式(11)计算,其中N是从标定靶标中提取出的特征点的总数。估计式(11)的最小值是一个非线性最优化过程,可以通过Levenberg-Marquardt算法计算。The parameters in formula (10) can be calculated by formula (11), where N is the total number of feature points extracted from the calibration target. Estimating the minimum value of equation (11) is a nonlinear optimization process, which can be calculated by the Levenberg-Marquardt algorithm.

通常情况下,当式(10)中的参数次数n达到3或者4时就可以达到比较好的拟合效果。当估计得出全部参数后,高度值ZC就可以利用式(10)获得,而XC和YC可以通过ZC、式(8)和相机小孔成像模型获得。Usually, when the number of parameters n in formula (10) reaches 3 or 4, a better fitting effect can be achieved. When all the parameters are estimated, the height value Z C can be obtained by using Equation (10), while X C and Y C can be obtained by Z C , Equation (8) and the camera pinhole imaging model.

为了降低算法复杂度,实现实时测量,这里考虑查找表LUT法,定义式(12):In order to reduce the complexity of the algorithm and realize real-time measurement, the look-up table LUT method is considered here, and the definition formula (12) is:

则本发明的新型条纹投影相位高度转换映射模型可简化为:Then the novel fringe projection phase-height conversion mapping model of the present invention can be simplified as:

预先计算出每个像素点的Z_LUT[u,v],测量时的计算量可以明显降低。同样,X和Y方向的测量也可以采用这种方式降低计算量,提高测量速度。The Z_LUT[u,v] of each pixel is pre-calculated, and the amount of calculation during measurement can be significantly reduced. Similarly, the measurement in the X and Y directions can also use this method to reduce the amount of calculation and improve the measurement speed.

本发明新型条纹投影相位高度转换映射模型的标定方法,如图3所示,具体步骤如下:The calibration method of the novel fringe projection phase-height conversion mapping model of the present invention, as shown in Figure 3, the specific steps are as follows:

步骤一,将标定靶标放在相机视场和投射器投影区域交界处的任意区域内。首先,投射器不需要发射任何投射条纹,相机拍摄标定靶标图像,用于提取标定靶标的特征点;然后,投射器发射投射条纹,同时相机拍摄图像,用于获取特征点的绝对相位。Step 1: Place the calibration target in any area at the junction of the camera's field of view and the projection area of the projector. First, the projector does not need to emit any projected fringes, and the camera captures the image of the calibration target to extract the feature points of the calibration target; then, the projector emits the projected fringes, and the camera takes images at the same time to obtain the absolute phase of the feature points.

步骤二,将标定靶标放置在相机视场和投射器投影区域交界处区域内另一位置,并保证标定靶标与之前的姿态不同,重复步骤一。Step 2, place the calibration target at another position in the junction of the camera field of view and the projection area of the projector, and ensure that the calibration target is different from the previous posture, and repeat step 1.

步骤三,重复步骤二直至采集到足够图像,一般是2~10组图像。实际上,只用2组图像就可以将所有的参数计算出来。尽管如此,通常至少需要5组图像以保证达到足够的准确度。Step 3, repeat step 2 until enough images are collected, generally 2 to 10 groups of images. In fact, all parameters can be calculated with only 2 sets of images. Nevertheless, usually at least 5 sets of images are required to achieve sufficient accuracy.

步骤四,提取特征点的图像坐标信息,并利用插值法计算对应特征点的绝对相位值,标定相机。Step 4, extract the image coordinate information of the feature points, calculate the absolute phase value of the corresponding feature points by interpolation method, and calibrate the camera.

步骤五,将所有特征点的坐标值转换到相机坐标系CCS下,利用特征点的信息(ZC;u v φ),计算出本发明新型条纹投影相位高度转换映射模型中的各个参数。Step 5: Convert the coordinate values of all feature points to the camera coordinate system CCS, and use the information (Z C ; uv φ) of the feature points to calculate each parameter in the new fringe projection phase-height conversion mapping model of the present invention.

如图4所示,将相机、投射器及其支架如图安装在光学平台上,其中相机和投影仪的相对位姿无严格要求。如图3中和上文描述的过程,由计算机控制投射器发射投射条纹,同时利用相机拍摄标定靶标图像;经过图像处理提取特征点图像坐标,将特征点图像坐标和特征点相机坐标系下的坐标带入本发明所提出的相位高度转换映射模型,求取参数;在计算出模型中的所有参数后,利用本模型测量如图5中的被测物。As shown in Figure 4, the camera, projector and its bracket are installed on the optical platform as shown in the figure, and the relative pose of the camera and projector is not strictly required. As shown in Figure 3 and the process described above, the computer controls the projector to emit projection stripes, and at the same time uses the camera to shoot the calibration target image; after image processing, the image coordinates of the feature points are extracted, and the image coordinates of the feature points and the image coordinates of the feature points in the camera coordinate system are combined. The coordinates are brought into the phase-height conversion mapping model proposed by the present invention to obtain parameters; after calculating all the parameters in the model, use this model to measure the measured object as shown in Fig. 5 .

按照上述方式,对本发明所提出模型及其标定方法进行实验验证,当模型中的非线性次数n=4时,标定所用特征点重建信息如图6所示,利用本模型进行三维测量的结果如图7所示,测量所用时间为11毫秒。According to the above method, the model proposed by the present invention and its calibration method are experimentally verified. When the nonlinear number n=4 in the model, the reconstruction information of the feature points used for calibration is shown in Figure 6, and the results of three-dimensional measurement using this model are shown in Figure 6. As shown in Figure 7, the time taken for the measurement is 11 milliseconds.

尽管上面结合附图对本发明的功能及工作过程进行了描述,但本发明并不局限于上述的具体功能和工作过程,上述的具体实施方式仅仅是示意性的,而不是限制性的,本领域的普通技术人员在本发明的启示下,在不脱离本发明宗旨和权利要求所保护的范围情况下,还可以做出很多形式,这些均属于本发明的保护之内。Although the function and working process of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the above-mentioned specific functions and working process, and the above-mentioned specific implementation is only illustrative, rather than limiting. Under the enlightenment of the present invention, those skilled in the art can also make many forms without departing from the spirit of the present invention and the scope protected by the claims, and these all belong to the protection of the present invention.

Claims (3)

1.一种新型条纹投影相位高度转换映射模型,其特征在于,相位高度转换映射模型为:1. A novel fringe projection phase-height conversion mapping model is characterized in that the phase-height conversion mapping model is: <mrow> <msub> <mi>Z</mi> <mi>C</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>b</mi> <mn>0</mn> </msub> <mo>+</mo> <mi>&amp;phi;</mi> </mrow> <mrow> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <mi>&amp;phi;</mi> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>n</mi> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>n</mi> <mo>-</mo> <mi>i</mi> </mrow> </munderover> <msub> <mi>k</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msup> <mi>u</mi> <mi>i</mi> </msup> <msup> <mi>v</mi> <mi>j</mi> </msup> </mrow> </mfrac> </mrow> <mrow><msub><mi>Z</mi><mi>C</mi></msub><mo>=</mo><mfrac><mrow><msub><mi>b</mi><mn>0</mn></msub><mo>+</mo><mi>&amp;phi;</mi></mrow><mrow><msub><mi>b</mi><mn>1</mn></msub><mo>+</mo><msub><mi>b</mi><mn>2</mn></msub><mi>&amp;phi;</mi><mo>+</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mi>n</mi></munderover><munderover><mo>&amp;Sigma;</mo><mrow><mi>j</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>n</mi><mo>-</mo><mi>i</mi></mrow></munderover><msub><mi>k</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><msup><mi>u</mi><mi>i</mi></msup><msup><mi>v</mi><mi>j</mi></msup></mrow></mfrac></mrow> 其中,in, kij=b3pij+b4qij k ij =b 3 p ij +b 4 q ij <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mi>u</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mo>=</mo> <msub> <mi>p</mi> <mn>00</mn> </msub> <mo>+</mo> <msub> <mi>p</mi> <mn>10</mn> </msub> <mi>u</mi> <mo>+</mo> <msub> <mi>p</mi> <mn>01</mn> </msub> <mi>v</mi> <mo>+</mo> <msub> <mi>p</mi> <mn>20</mn> </msub> <msup> <mi>u</mi> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>p</mi> <mn>11</mn> </msub> <mi>u</mi> <mi>v</mi> <mo>+</mo> <msub> <mi>p</mi> <mn>02</mn> </msub> <msup> <mi>v</mi> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>p</mi> <mn>30</mn> </msub> <msup> <mi>u</mi> <mn>3</mn> </msup> <mo>+</mo> <mn>...</mn> <mo>=</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>n</mi> </munderover> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>n</mi> <mo>-</mo> <mi>i</mi> </mrow> </munderover> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msup> <mi>u</mi> <mi>i</mi> </msup> <msup> <mi>v</mi> <mi>i</mi> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>v</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mo>=</mo> <msub> <mi>q</mi> <mn>00</mn> </msub> <mo>+</mo> <msub> <mi>q</mi> <mn>10</mn> </msub> <mi>u</mi> <mo>+</mo> <msub> <mi>q</mi> <mn>01</mn> </msub> <mi>v</mi> <mo>+</mo> <msub> <mi>q</mi> <mn>20</mn> </msub> <msup> <mi>u</mi> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>q</mi> <mn>11</mn> </msub> <mi>u</mi> <mi>v</mi> <mo>+</mo> <msub> <mi>q</mi> <mn>02</mn> </msub> <msup> <mi>v</mi> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>q</mi> <mn>30</mn> </msub> <msup> <mi>u</mi> <mn>3</mn> </msup> <mo>+</mo> <mn>...</mn> <mo>=</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>n</mi> </munderover> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>n</mi> <mo>-</mo> <mi>i</mi> </mrow> </munderover> <msub> <mi>q</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msup> <mi>u</mi> <mi>i</mi> </msup> <msup> <mi>v</mi> <mi>i</mi> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "{" close = ""><mtable><mtr><mtd><mrow><msup><mi>u</mi><mrow><mo>&amp;prime;</mo><mo>&amp;prime;</mo></mrow></msup><mo>=</mo><msub><mi>p</mi><mn>00</mn></msub><mo>+</mo><msub><mi>p</mi><mn>10</mn></msub><mi>u</mi><mo>+</mo><msub><mi>p</mi><mn>01</mn></msub><mi>v</mi><mo>+</mo><msub><mi>p</mi><mn>20</mn></msub><msup><mi>u</mi><mn>2</mn></msup><mo>+</mo><msub><mi>p</mi><mn>11</mn></msub><mi>u</mi><mi>v</mi><mo>+</mo><msub><mi>p</mi><mn>02</mn></msub><msup><mi>v</mi><mn>2</mn></msup><mo>+</mo><msub><mi>p</mi><mn>30</mn></msub><msup><mi>u</mi><mn>3</mn></msup><mo>+</mo><mn>...</mn><mo>=</mo><munderover><mi>&amp;Sigma;</mi><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mi>n</mi></munderover><munderover><mi>&amp;Sigma;</mi><mrow><mi>j</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>n</mi><mo>-</mo><mi>i</mi></mrow></munderover><msub><mi>p</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><msup><mi>u</mi><mi>i</mi></msup><msup><mi>v</mi><mi>i</mi></msup></mrow></mtd></mtr><mtr><mtd><mrow><msup><mi>v</mi><mrow><mo>&amp;prime;</mo><mo>&amp;prime;</mo></mrow></msup><mo>=</mo><msub><mi>q</mi><mn>00</mn></msub><mo>+</mo><msub><mi>q</mi><mn>10</mn></msub><mi>u</mi><mo>+</mo><msub><mi>q</mi><mn>01</mn></msub><mi>v</mi><mo>+</mo><msub><mi>q</mi><mn>20</mn></msub><msup><mi>u</mi><mn>2</mn></msup><mo>+</mo><msub><mi>q</mi><mn>11</mn></msub><mi>u</mi><mi>v</mi><mo>+</mo><msub><mi>q</mi><mn>02</mn></msub><msup><mi>v</mi><mn>2</mn></msup><mo>+</mo><msub><mi>q</mi><mn>30</mn></msub><msup><mi>u</mi><mn>3</mn></msup><mo>+</mo><mn>...</mn><mo>=</mo><munderover><mi>&amp;Sigma;</mi><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mi>n</mi></munderover><munderover><mi>&amp;Sigma;</mi><mrow><mi>j</mi><mo>=</mo><mn>0</mn></mi>mrow><mrow><mi>n</mi><mo>-</mo><mi>i</mi></mrow></munderover><msub><mi>q</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><msup><mi>u</mi><mi>i</mi></msup><msup><mi>v</mi><mi>i</mi></msup></mrow></mtd></mtr></mtable></mfenced> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>b</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>&amp;phi;</mi> <mn>0</mn> </msub> <mo>-</mo> <mfrac> <msub> <mi>t</mi> <mi>X</mi> </msub> <mrow> <msub> <mi>wt</mi> <mn>2</mn> </msub> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>X</mi> <mi>P</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;phi;</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>wt</mi> <mi>Z</mi> </msub> </mrow> </mfrac> </mrow> </mtd> <mtd> <mrow> <msub> <mi>b</mi> <mn>3</mn> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>f</mi> <mi>u</mi> </msub> <msub> <mi>wt</mi> <mi>Z</mi> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <msub> <mi>u</mi> <mi>o</mi> </msub> <mrow> <msub> <mi>f</mi> <mi>u</mi> </msub> <msub> <mi>wt</mi> <mi>Z</mi> </msub> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>sv</mi> <mi>o</mi> </msub> </mrow> <mrow> <msub> <mi>f</mi> <mi>v</mi> </msub> <msub> <mi>wt</mi> <mi>Z</mi> </msub> </mrow> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>&amp;phi;</mi> <mn>0</mn> </msub> <msub> <mi>t</mi> <mi>Z</mi> </msub> </mfrac> </mrow> </mtd> <mtd> <mrow> <msub> <mi>b</mi> <mn>4</mn> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mi>s</mi> <mrow> <msub> <mi>f</mi> <mi>v</mi> </msub> <msub> <mi>wt</mi> <mi>Z</mi> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mn>1</mn> <msub> <mi>t</mi> <mi>Z</mi> </msub> </mfrac> </mrow> </mtd> <mtd> <mrow></mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "{" close = ""><mtable><mtr><mtd><mrow><msub><mi>b</mi><mn>0</mn></msub><mo>=</mo><mo>-</mo><msub><mi>&amp;phi;</mi><mn>0</mn></msub><mo>-</mo><mfrac><msub><mi>t</mi><mi>X</mi></msub><mrow><msub><mi>wt</mi><mn>2</mn></msub></mrow></mfrac><mo>+</mo><mfrac><mrow><msub><mi>X</mi><mi>P</mi></msub><mrow><mo>(</mo><msub><mi>&amp;phi;</mi><mn>0</mn></msub><mo>)</mo></mrow></mrow><mrow><msub><mi>wt</mi><mi>Z</mi></msub></mrow></mfrac></mrow></mtd><mtd><mrow><msub><mi>b</mi><mn>3</mn></msub><mo>=</mo><mfrac><mn>1</mn><mrow><msub><mi>f</mi><mi>u</mi></msub><msub><mi>wt</mi><mi>Z</mi></msub></mrow></mfrac></mrow></msub>mtd></mtr><mtr><mtd><mrow><msub><mi>b</mi><mn>1</mn></msub><mo>=</mo><mo>-</mo><mfrac><msub><mi>u</mi><mi>o</mi></msub><mrow><msub><mi>f</mi><mi>u</mo>mi></msub><msub><mi>wt</mi><mi>Z</mi></msub></mrow></mfrac><mo>+</mo><mfrac><mrow><msub><mi>sv</mi><mi>o</mi></msub></mrow><mrow><msub><mi>f</mi><mi>v</mi></msub><msub><mi>wt</mi><mi>Z</mi></mrow>msub></mrow></mfrac><mo>+</mo><mfrac><msub><mi>&amp;phi;</mi><mn>0</mn></msub><msub><mi>t</mi><mi>Z</mi></msub></mfrac></mrow></mtd><mtd><mrow><msub><mi>b</mi><mn>4</mn></msub><mo>=</mo><mo>-</mo><mfrac><mi>s</mi><mrow><msub><mi>f</mi><mi>v</mi></msub><msub><mi>wt</mi><mi>Z</mi></msub></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>b</mi><mn>2</mn></msub><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><msub><mi>t</mi><mi>Z</mi></msub></mfrac></mrow></mtd><mtd><mrow></mrow></mtd></mtr></mtable></mfenced> [u v]T代表未经畸变校正的图像坐标;[u" v"]T是变换后的图像坐标;投射器坐标系PCS中圆点OP代表发光点,XP轴平行于投射条纹相位变化的方向,YP轴垂直投射条纹相位变化的方向,ZP轴垂直于投射条纹的相平面,在投射器坐标系PCS中任意一点的坐标表示为[XPYP ZP]T,在投射器坐标系PCS中,同一条光线上的空间点相位相同,均为φ,在同一高度ZP上,相位值从φ0变化到φ1,对应的XP变化范围是[XP0),XP1)];w是尺度因子;TP是平移向量,TP=[tX tY tZ]T;[fu fv]T代表镜头的焦距,[uo vo]T是图像中心坐标;s是图像坐标轴的扭曲系数。[uv] T represents the image coordinates without distortion correction; [u"v"] T is the transformed image coordinates ; the dot OP in the projector coordinate system PCS represents the luminous point, and the X P axis is parallel to the projected fringe phase change The direction of the Y P axis is perpendicular to the direction of the phase change of the projected fringe, and the Z P axis is perpendicular to the phase plane of the projected fringe. The coordinates of any point in the projector coordinate system PCS are expressed as [X P Y P Z P ] T , in the projected In the sensor coordinate system PCS, the phases of the spatial points on the same ray are the same, φ, and at the same height Z P , the phase value changes from φ 0 to φ 1 , and the corresponding X P variation range is [X P0 ),X P1 )]; w is the scale factor; T P is the translation vector, T P =[t X t Y t Z ] T ; [fu f v ] T represents the focal length of the lens, [ u o v o ] T is the center coordinate of the image; s is the distortion coefficient of the image coordinate axis. 2.根据权利要求1所述的新型条纹投影相位高度转换映射模型,其特征在于,为了降低算法复杂度,实现实时测量,利用查找表LUT法,定义2. the novel fringe projection phase-height conversion mapping model according to claim 1 is characterized in that, in order to reduce algorithm complexity, realize real-time measurement, utilize look-up table LUT method, define <mrow> <mi>Z</mi> <mo>_</mo> <mi>L</mi> <mi>U</mi> <mi>T</mi> <mo>&amp;lsqb;</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>&amp;rsqb;</mo> <mo>=</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>n</mi> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>n</mi> <mo>-</mo> <mi>i</mi> </mrow> </munderover> <msub> <mi>k</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msup> <mi>u</mi> <mi>i</mi> </msup> <msup> <mi>v</mi> <mi>j</mi> </msup> </mrow> <mrow><mi>Z</mi><mo>_</mo><mi>L</mi><mi>U</mi><mi>T</mi><mo>&amp;lsqb;</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>&amp;rsqb;</mo><mo>=</mo><msub><mi>b</mi><mn>1</mn></msub><mo>+</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mi>n</mi></munderover><munderover><mo>&amp;Sigma;</mo><mrow><mi>j</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>n</mi><mo>-</mo><mi>i</mi></mrow></munderover><msub><mi>k</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><msup><mi>u</mi><mi>i</mi></msup><msup><mi>v</mi><mi>j</mi></msup></mrow> 则高度转换映射模型Zc简化为:Then the height conversion mapping model Zc is simplified as: <mrow> <msub> <mi>Z</mi> <mi>C</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>b</mi> <mn>0</mn> </msub> <mo>+</mo> <mi>&amp;phi;</mi> </mrow> <mrow> <msub> <mi>b</mi> <mn>2</mn> </msub> <mi>&amp;phi;</mi> <mo>+</mo> <mi>Z</mi> <mo>_</mo> <mi>L</mi> <mi>U</mi> <mi>T</mi> <mo>&amp;lsqb;</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>&amp;rsqb;</mo> </mrow> </mfrac> </mrow> <mrow><msub><mi>Z</mi><mi>C</mi></msub><mo>=</mo><mfrac><mrow><msub><mi>b</mi><mn>0</mn></msub><mo>+</mo><mi>&amp;phi;</mi></mrow><mrow><msub><mi>b</mi><mn>2</mn></msub><mi>&amp;phi;</mi><mo>+</mo><mi>Z</mi><mo>_</mo><mi>L</mi><mi>U</mi><mi>T</mi><mo>&amp;lsqb;</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>&amp;rsqb;</mo></mrow></mfrac></mrow> 3.一种上述权利要求1和2所述新型条纹投影相位高度转换映射模型的标定方法,其特征在于,包括以下步骤:3. a calibration method of the novel fringe projection phase-height conversion mapping model described in claims 1 and 2, is characterized in that, comprises the following steps: 步骤一,将标定靶标放在相机视场和投射器投影区域交界处的区域内,相机拍摄标定靶标图像,然后投射器发射投射条纹,同时相机拍摄图像;Step 1, place the calibration target in the area at the junction of the camera field of view and the projection area of the projector, the camera captures the image of the calibration target, then the projector emits projection stripes, and the camera captures images at the same time; 步骤二,将标定靶标放置在相机视场和投射器投影区域交界处区域内另一位置,且标定靶标与之前的姿态不同,重复步骤一;Step 2, place the calibration target at another position in the junction of the camera field of view and the projection area of the projector, and the calibration target is different from the previous posture, repeat step 1; 步骤三,重复步骤二直至采集到足够图像,一般是2~10组图像;Step 3, repeat step 2 until enough images are collected, usually 2 to 10 groups of images; 步骤四,提取特征点的图像坐标信息,并利用插值法计算对应特征点的绝对相位值,标定相机;Step 4, extract the image coordinate information of the feature points, and use the interpolation method to calculate the absolute phase value of the corresponding feature points, and calibrate the camera; 步骤五,将所有特征点的坐标值转换到相机坐标系CCS下,利用特征点的信息(ZC;u vφ),计算出本发明新型条纹投影相位高度转换映射模型中的各个参数。Step 5: Convert the coordinate values of all feature points to the camera coordinate system CCS, and use the information (Z C ; u v φ) of the feature points to calculate each parameter in the novel fringe projection phase-height conversion mapping model of the present invention.
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