CN105976374A

CN105976374A - Field-related distortion calibration method of photogrammetric camera

Info

Publication number: CN105976374A
Application number: CN201610297127.3A
Authority: CN
Inventors: 董明利; 孙鹏; 吕乃光; 王君; 燕必希; 庄炜
Original assignee: Beijing Information Science and Technology University
Current assignee: Beijing Information Science and Technology University
Priority date: 2016-05-06
Filing date: 2016-05-06
Publication date: 2016-09-28
Anticipated expiration: 2036-05-06
Also published as: CN105976374B

Abstract

The invention provides a method for calibrating field-dependent distortion of a photogrammetry camera in a defocused state, comprising the steps of: a) establishing a backlight reflection coplanar linear array field for calibrating field-dependent distortion; b) according to the depth of field of the measurement environment Adjust the focus state of the camera to be calibrated and the distance requirements, and fix the imaging system of the camera so that it cannot be adjusted; c) Establish a field-related radial distortion model under any focus state; d) Calibrate the described Field-related distortion calibration parameters, that is, radial distortion parameters, and deduce the distortion parameters of spatial points on the camera image plane at any other distance; e) use the radial distortion parameters obtained in step d to calculate the radial distortion parameters on different imaging radii distortion.

Description

Field-dependent distortion calibration method for photogrammetric cameras

技术领域technical field

本发明涉及一种相机的畸变参数标定的方法，尤其涉及使用多台工业相机进行大尺寸、动态三维测量时的摄影测量相机的场相关畸变标定方法。The invention relates to a camera distortion parameter calibration method, in particular to a field-related distortion calibration method of a photogrammetry camera when a plurality of industrial cameras are used for large-scale and dynamic three-dimensional measurement.

背景技术Background technique

伴随着工业的不断进步，工业同航空航天、军事、工程建设、新能源开发之间的关系越来越紧密，各种大尺寸、高精密、实时动态甚至是非接触的测量需求也日益出现并增加，摄影测量已经在国外相关领域得到了广泛的尝试和应用。With the continuous progress of industry, the relationship between industry and aerospace, military, engineering construction, and new energy development is getting closer and closer, and various large-scale, high-precision, real-time dynamic and even non-contact measurement requirements are also emerging and increasing. , photogrammetry has been widely tried and applied in foreign related fields.

目前，应用最为广泛的非线性畸变模型包含了径向畸变、离心畸变以及多样的附加畸变。将这种模型及标定方法直接应用于大尺寸立体测量中，会产生巨大的误差，根本原因在于忽略了畸变量同物距以及对焦状态之间的关系，错误地认为畸变参数恒定。At present, the most widely used nonlinear distortion model includes radial distortion, centrifugal distortion and various additional distortions. Applying this model and calibration method directly to large-scale stereo measurement will produce huge errors. The fundamental reason is that the relationship between distortion, object distance and focus state is ignored, and the distortion parameter is mistakenly considered constant.

在这一问题上，传统的摄影测量很好地解决了这一问题，由于有规划合理、冗余度高的多站位测量网络，光束平差可以实现测量期间相机内参数的自标定，标定结果同被测距离、测量范围甚至环境因素紧密相关。On this issue, traditional photogrammetry has solved this problem very well. Due to the multi-site measurement network with reasonable planning and high redundancy, beam adjustment can realize the self-calibration of camera internal parameters during the measurement period. Calibration The results are closely related to the measured distance, measurement range and even environmental factors.

本研究针对前述应用领域中指出的固定对焦状态的工业测量相机，研究物距变化对成像点畸变参数的模型，提出在更为普适的离焦状态下标定此畸变模型的方法。This study aims at the industrial measurement camera with a fixed focus state pointed out in the aforementioned application fields, studies the model of the distortion parameter of the imaging point caused by the change of the object distance, and proposes a method for calibrating the distortion model in a more general defocus state.

发明内容Contents of the invention

为了解决上述技术问题，本发明提供一种摄影测量相机的场相关畸变标定方法，步骤为：a)建立用于场相关畸变标定的回光反射共面直线阵列场；b)根据测量环境景深和距离要求调整待标定相机对焦状态，并固定相机的成像系统，使之无法调焦；c)建立任意对焦状态下，场相关的径向畸变模型；d)在两个不同距离上标定所述场相关畸变标定参数，即径向畸变参数，并推导得到任意其他距离上空间点在相机像面上的畸变参数；e)利用步骤d中获取的径向畸变参数计算不同成像半径上的径向畸变量。In order to solve the above-mentioned technical problems, the present invention provides a method for calibrating field-dependent distortion of a photogrammetric camera, the steps of which are: a) establishing a coplanar linear array field of return light reflection for calibrating field-dependent distortion; b) according to the depth of field of the measurement environment and The distance requires adjusting the focus state of the camera to be calibrated, and fixing the imaging system of the camera so that it cannot be adjusted; c) Establishing a field-related radial distortion model under any focus state; d) Calibrating the field at two different distances Relevant distortion calibration parameters, that is, radial distortion parameters, and deriving the distortion parameters of spatial points on the camera image plane at any other distance; e) using the radial distortion parameters obtained in step d to calculate the radial distortion on different imaging radii quantity.

优选地，所述步骤a)中建立场相关畸变标定场的步骤为:Preferably, the step of establishing a field-dependent distortion calibration field in the step a) is:

a1)展开框架，并用连接杆支撑所述框架的活动关节，保持所述框架稳定；a1) unfolding the frame, and supporting the movable joints of the frame with connecting rods to keep the frame stable;

a2)将直线材料竖直平行固定于所述框架上下两端，并拉伸所述直线材料，保持所述直线材料的直线度；a2) fixing the linear material vertically and parallel to the upper and lower ends of the frame, and stretching the linear material to maintain the straightness of the linear material;

a3)在所述连接杆上布置所述编码点，用于测量并调整标定时相机光轴的角度。a3) Arranging the coding points on the connecting rod for measuring and adjusting the angle of the optical axis of the camera during calibration.

优选地，所述框架为拉伸框架，能够收缩及展开；所述框架展开后尺寸至少为长3米、高2米。Preferably, the frame is a tensile frame, capable of contraction and expansion; the size of the frame after expansion is at least 3 meters long and 2 meters high.

优选地，所述框架的背景布置为黑色吸光绒布，用于减轻环境光带来的成像背景噪声。Preferably, the background of the frame is arranged as black light-absorbing flannelette, which is used to reduce imaging background noise caused by ambient light.

优选地，所述直线材料设置为具有宽度的回光反射线条，所述回光反射线条的宽度由标定时相机距离标定场的距离决定。Preferably, the straight line material is set as a retroreflective line with a width, and the width of the retroreflective line is determined by the distance between the camera and the calibration field during calibration.

优选地，所述回光反射线条的反光材料为玻璃微珠。Preferably, the reflective material of the retroreflective lines is glass beads.

优选地，所述直线材料的拉伸方法为在所述框架的上下两端布置G字夹，通过所述G字夹对所述直线材料进行拉伸。Preferably, the stretching method of the linear material is to arrange G-shaped clips at the upper and lower ends of the frame, and stretch the linear material through the G-shaped clips.

优选地，所述步骤c)中建立径向畸变模型的方法为：Preferably, the method for establishing the radial distortion model in the step c) is:

c1)设相机相面对焦于S距离，被测点位于距相机S₁处的物面上，获取径向畸变量；c1) Assuming that the camera phase plane focuses on the S distance, the measured point is located on the object surface at S ₁ from the camera, and the radial distortion is obtained;

c2)设相机对焦于S₁物距时焦面的径向畸变参数为获取此对焦状态下像面上径向距离为的任意像点处的径向畸变量；c2) Suppose the radial distortion parameter of the focal plane when the camera focuses on the S ₁ object distance is Obtain the radial distance on the image plane in this focus state as The radial distortion at any image point of ;

c3)再设相机像面对焦于距离S处，利用离焦畸变量相似性分析获取S₁距离平面上的物点在相机像面上的畸变量。c3) Let the camera image plane focus on the distance S, and use the similarity analysis of the defocus distortion to obtain the distortion of the object point _on the S1 distance plane on the camera image plane.

优选地，所述步骤d)中径向畸变参数标定方法为：Preferably, the radial distortion parameter calibration method in the step d) is:

d1)设相机相面对焦于S距离，利用共面直线阵列场标定两个距离S₁和S₂上的径向畸变参数，分别为以及 d1) Assuming that the camera phase plane focuses _on the distance S, use the coplanar linear array field to calibrate the radial distortion parameters at the _two distances S1 and S2, respectively as well as

d2)设已知镜头焦距f，在标定时测量同时记录下S₁和S₂的精确值，求取像距和 _d2 ) Assuming that the focal length f of the lens is known, measure and record the precise values _of S1 and S2 at the same time during calibration, and calculate the image distance and

d3)利用步骤C中的结论，建立离焦状态下径向畸变参数的标定结果以及同对焦状态下的畸变参数以及之间的数学关系；d3) Using the conclusion in step C, establish the calibration result of the radial distortion parameter in the defocused state as well as Distortion parameters in the same focus state as well as the mathematical relationship between

d4)根据Brown的模型，由对焦状态下两个距离上的畸变参数，获取对焦于任意距离S′处的相机像面畸变量δ_rs′；d4) According to Brown's model, obtain the image plane distortion δ _rs' of the camera focusing at any distance S' from the distortion parameters on the two distances in the focusing state;

其中，对焦于两距离上的畸变参数与相应的离焦畸变参数之间的关系为已知，通过d3)描述。Wherein, the relationship between the distortion parameters focusing on two distances and the corresponding defocus distortion parameters is known, described by d3).

d5)再将畸变量δ_rs′离焦至相机像面上,主距为C_s；d5) Defocus the distortion amount δ _rs' to the camera image plane, and the principal distance is C _s ;

d6)计算各径向畸变参数：d6) Calculate each radial distortion parameter:

d7)计算物距在S′，并求得像面对焦于S距离时的径向畸变参数。d7) Calculate the object distance at S', and obtain the radial distortion parameter when the image plane is focused at the S distance.

总结上述方法，本发明的摄影测量相机的场相关畸变标定方法解决了以下问题：克服了相机标定时对于对焦的依赖，简化了标定过程，不依赖准确的镜头焦距和物距测量，消除离焦带来的系统误差；标定相机完毕即可以固定相机主距，在后续测量中保证测量精度的稳定；模型非常适合于高精度三维测量工业相机的标定，对于在工业领域推广大尺寸的动态摄影测量技术具有理论和实践意义。Summarizing the above methods, the field-dependent distortion calibration method of the photogrammetry camera of the present invention solves the following problems: it overcomes the dependence on focusing during camera calibration, simplifies the calibration process, does not rely on accurate lens focal length and object distance measurement, and eliminates defocus The system error brought about; the main distance of the camera can be fixed after the camera is calibrated to ensure the stability of the measurement accuracy in the subsequent measurement; the model is very suitable for the calibration of high-precision three-dimensional measurement industrial cameras, and is very useful for the promotion of large-scale dynamic photogrammetry in the industrial field Technology has theoretical and practical implications.

附图说明Description of drawings

为了更清楚的说明本发明实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单的介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他附图。In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. For those skilled in the art, other drawings can also be obtained according to these drawings without creative work.

图1为本发明摄影测量相机的场相关畸变标定方法的流程图；FIG. 1 is a flow chart of a method for calibrating field-dependent distortion of a photogrammetric camera according to the present invention;

图2a为本发明的步骤a)中建立的用于场相关畸变标定的回光反射共面直线阵列场；Fig. 2 a is the retroreflective coplanar linear array field used for field-dependent distortion calibration established in step a) of the present invention;

图2b为本发明的步骤a)中建立的用于场相关畸变标定的回光反射共面直线阵列场中的用G字夹固定直线材料的布置图。Fig. 2b is a layout diagram of fixing linear materials with G-shaped clips in the retroreflective coplanar linear array field established in step a) of the present invention for calibrating field-dependent distortion.

图2c为框架的展开状态；Figure 2c is the unfolded state of the frame;

图3为场相关的径向畸变模型的建模原理图。Fig. 3 is a modeling schematic diagram of a field-dependent radial distortion model.

具体实施方式detailed description

通过参考示范性实施例，本发明的目的和功能以及用于实现这些目的和功能的方法将得以阐明。然而，本发明并不受限于以下所公开的示范性实施例，可以通过不同形式来对其加以实现。说明书的实质仅仅是帮助相关领域技术人员综合理解本发明的具体细节。The objects and functions of the present invention and methods for achieving the objects and functions will be clarified by referring to the exemplary embodiments. However, the present invention is not limited to the exemplary embodiments disclosed below, and may be implemented in various forms. The essence of the description is only to help those skilled in the relevant art comprehensively understand the specific details of the present invention.

本发明针对固定对焦状态的工业测量相机，研究物距变化对成像点畸变参数的模型，提出在更为普适的离焦状态下标定此畸变模型的方法。The invention studies the model of the distortion parameter of the imaging point caused by the change of the object distance, and proposes a method for calibrating the distortion model in a more general defocus state, aiming at the industrial measurement camera in the fixed focus state.

本发明中的被测对象体积大，相机光轴方向深度范围大，不同距离上的目标点在成像面上具有不同的畸变参数，因此需要在特殊的大型标定场中进行标定；用到的工业相机不具备自动对焦能力，依靠人工看图调焦必然存在0.5至1个像素的对焦误差，仿真分析指出，这种对焦误差会给小光圈相机带来巨大的标定误差；摄影测量需要保证相机内部参数的稳定，依靠更改像距(调焦)来获得焦面位置是不利于保证测量精度的。因此本发明研究一种相机定主距、离焦状态下，标定同物距相关的畸变参数的模型和方法。The object to be measured in the present invention has a large volume and a large depth range in the direction of the optical axis of the camera, and target points at different distances have different distortion parameters on the imaging surface, so it needs to be calibrated in a special large-scale calibration field; the used industrial The camera does not have the ability to automatically focus, and there must be a focus error of 0.5 to 1 pixel when relying on manual image adjustment. The simulation analysis points out that this focus error will bring a huge calibration error to the camera with a small aperture; photogrammetry needs to ensure that the camera’s internal The stability of the parameters, relying on changing the image distance (focusing) to obtain the focal plane position is not conducive to ensuring the measurement accuracy. Therefore, the present invention researches a model and method for calibrating distortion parameters related to object distance when the camera is in the state of fixed main distance and defocus.

如图1所示，为本发明摄影测量相机的场相关畸变标定方法的流程图，包括步骤：As shown in Figure 1, it is a flow chart of the field-related distortion calibration method of the photogrammetry camera of the present invention, including steps:

步骤101：建立用于场相关畸变标定的回光反射共面直线阵列场；Step 101: Establishing a coplanar linear array field of return light reflection for calibration of field-dependent distortion;

如图2a所示，为步骤a)中所述的用于场相关畸变标定的回光反射共面直线阵列场，包括框架201、直线材料202、编码点203、黑色吸光绒布204、连接杆205以及G字夹206；As shown in Figure 2a, it is the retroreflective coplanar linear array field used for field-dependent distortion calibration described in step a), including a frame 201, a straight line material 202, a code point 203, a black light-absorbing fleece 204, and a connecting rod 205 And the G word folder 206;

图2b为用G字夹固定直线材料的布置图；Figure 2b is a layout diagram of fixing straight line materials with G-shaped clips;

图2c为框架201的展开状态，其中连接杆205用于支撑框架201。FIG. 2 c is the unfolded state of the frame 201 , wherein the connecting rod 205 is used to support the frame 201 .

根据本发明的一个实施例，所述步骤a)中建立场相关畸变标定场的步骤为:According to an embodiment of the present invention, the step of establishing a field-dependent distortion calibration field in the step a) is:

a1)展开框架201，并用连接杆205支撑所述框架201的活动关节207，保持所述框架201稳定；a1) Expand the frame 201, and support the movable joint 207 of the frame 201 with the connecting rod 205, to keep the frame 201 stable;

a2)将直线材料202竖直平行固定于所述框架201上下两端，并拉伸所述直线材料202，保持所述直线材料202的直线度；a2) fixing the linear material 202 vertically and parallelly to the upper and lower ends of the frame 201, and stretching the linear material 202 to maintain the straightness of the linear material 202;

a3)在所述连接杆205上布置所述编码点203，用于测量并调整标定时相机光轴的角度。a3) Arranging the code point 203 on the connecting rod 205 for measuring and adjusting the angle of the optical axis of the camera during calibration.

根据本发明的一个实施例，所述框架为拉伸框架，能够收缩及展开；所述框架201展开后尺寸至少为长3米、高2米，如图2c所示。According to an embodiment of the present invention, the frame is a tensile frame that can be contracted and expanded; the frame 201 is at least 3 meters long and 2 meters high after being expanded, as shown in FIG. 2c.

根据本发明的一个实施例，所述框架201的背景布置为黑色吸光绒布204,用于减轻环境光带来的成像背景噪声。According to an embodiment of the present invention, the background of the frame 201 is arranged as a black light-absorbing fleece 204, which is used to reduce imaging background noise caused by ambient light.

根据本发明的一个实施例，所述直线材料202设置为具有宽度的回光反射线条，回光反射线条的宽度由标定时相机距离标定场的距离决定。According to an embodiment of the present invention, the straight line material 202 is set as a retroreflective line with a width, and the width of the retroreflective line is determined by the distance between the camera and the calibration field during calibration.

根据本发明的一个实施例，所述回光反射线条的反光材料为玻璃微珠。According to an embodiment of the present invention, the reflective material of the retroreflective lines is glass beads.

根据本发明的一个实施例，所述直线材料202的拉伸方法为在所述框架201的上下两端布置G字夹206，可见图2b所示，为用G字夹固定直线材料的布置图；通过所述G字夹203对所述直线材料202进行拉伸。According to an embodiment of the present invention, the stretching method of the linear material 202 is to arrange G-shaped clips 206 at the upper and lower ends of the frame 201, as shown in FIG. Stretching the linear material 202 through the G-shaped clamp 203 ;

步骤102：根据测量环境景深和距离要求调整待标定相机对焦状态，并固定相机的成像系统，使之无法调焦；Step 102: Adjust the focus state of the camera to be calibrated according to the depth of field and distance requirements of the measurement environment, and fix the imaging system of the camera so that it cannot be adjusted;

步骤103：建立任意对焦状态下，场相关的径向畸变模型；Step 103: Establishing a field-dependent radial distortion model in any focusing state;

如图3所示，为场相关的径向畸变模型的建模原理图：As shown in Figure 3, it is the modeling schematic diagram of the field-related radial distortion model:

其中：物空间点P位于距离相机S1处的物面上，C_s1是其满足高斯成像公式的焦平面；Cs是相机实际的像面位置。是焦面上像点处的径向畸变量，是经过光线传播至实际像面上的径向畸变量。我们可以标定C_s1焦面上的径向畸变参数，需要通过相似三角形分析得到实际Cs像面上对应的畸变参数和畸变量。关于两者之间的联系以及两个像面上径向畸变量之间的关系，通过下面的推演可以得到。Among them: the object space point P is located on the object plane at a distance of S1 from the camera, C _s1 is the focal plane satisfying the Gaussian imaging formula; Cs is the actual image plane position of the camera. is the radial distortion at the image point on the focal plane, is the amount of radial distortion that propagates through the light to the actual image plane. We can calibrate the radial distortion parameters on the _Cs1 focal plane, and we need to obtain the corresponding distortion parameters and distortion amounts on the actual Cs image plane through similar triangle analysis. The relationship between the two and the relationship between the radial distortion on the two image planes can be obtained through the following deduction.

根据本发明的一个实施例，所述步骤103中建立径向畸变模型的方法为：According to an embodiment of the present invention, the method for establishing the radial distortion model in step 103 is:

c1)设相机相面对焦于S距离，被测点位于距相机S₁处的物面上，径向畸变量通过下述多项式描述：c1) Assuming that the camera phase plane is focused at a distance S, the measured point is located on the object surface at _a distance S1 from the camera, and the radial distortion is described by the following polynomial:

δ_r＝k₁r³+k₂r⁵+k₃r⁷ δ _r =k ₁ r ³ +k ₂ r ⁵ +k ₃ r ⁷

c2)设相机对焦于S₁物距时焦面的径向畸变参数为获取此对焦状态下像面上径向距离为的任意像点处的径向畸变量为：c2) Suppose the radial distortion parameter of the focal plane when the camera focuses on the S ₁ object distance is Obtain the radial distance on the image plane in this focus state as The radial distortion at any image point of is:

${δ δ}_{{rs rs}_{11}} = = {k k}_{11 {s the s}_{11}} {r r}_{{s the s}_{11}}^{33} + + {k k}_{22 {s the s}_{11}} {r r}_{{s the s}_{11}}^{55} + + {k k}_{33 {s the s}_{11}} {r r}_{{s the s}_{11}}^{77}$

c3)再设相机像面对焦于距离S处，利用离焦畸变量相似性分析获取S₁距离平面上的物点在相机像面上的畸变量为：c3) Let the camera image plane focus on the distance S, and use the defocus distortion similarity analysis to obtain the distortion of the object point on the camera image plane _on the S1 distance plane as:

${δ δ}_{{rss rss}_{11}} \cdot \cdot {γ γ}_{{ss ss}_{11}} \cdot &Center Dot; {δ δ}_{{r r}_{{s the s}_{11}}}$

其中，是一比例系数，与C_s分别是对焦于S₁与S距离上的高斯成像模型的像距。同时可知道：in, is a proportionality coefficient, and C _s are the image distances of the Gaussian imaging model focusing on S ₁ and S distances, respectively. Also know:

${r r}_{{s the s}_{11}} = = {γ γ}_{{ss ss}_{11}} \cdot \cdot {r r}_{s the s}$

c4)将步骤c3)中的畸变量公式改写为：c4) rewrite the distortion formula in step c3) as:

$\begin{matrix} {δ δ}_{{rss rss}_{11}} = = {γ γ}_{{ss ss}_{11}} \cdot \cdot {δ δ}_{{r r}_{{s the s}_{11}}} = = {γ γ}_{{ss ss}_{11}}^{22} {k k}_{11 {s the s}_{11}} {r r}_{s the s}^{33} + + {γ γ}_{{ss ss}_{11}}^{44} {k k}_{22 {s the s}_{11}} {r r}_{s the s}^{55} + + {γ γ}_{{ss ss}_{11}}^{66} {k k}_{33 {s the s}_{11}} {r r}_{s the s}^{77} \\ = = \frac{{C C}_{{s the s}_{11}}^{22}}{{C C}_{s the s}^{22}} {k k}_{11 {s the s}_{11}} {r r}_{s the s}^{33} + + \frac{{C C}_{{s the s}_{11}}^{44}}{{C C}_{s the s}^{44}} {k k}_{22 {s the s}_{11}} {r r}_{s the s}^{55} + + \frac{{C C}_{{s the s}_{11}}^{66}}{{C C}_{s the s}^{66}} {k k}_{33 {s the s}_{11}} {r r}_{s the s}^{77} \\ = = {k k}_{11 {ss ss}_{11}} {r r}_{s the s}^{33} + + {k k}_{22 {ss ss}_{11}} {r r}_{s the s}^{55} + + {k k}_{33 {ss ss}_{11}} {r r}_{s the s}^{77} \end{matrix}$

由此可见，固定主距时，径向畸变同物距是紧密相关的。It can be seen that when the main distance is fixed, the radial distortion is closely related to the object distance.

由于本发明中的径向畸变同物距相关，则需要标定两个距离上的径向畸变参数，进一步解算其他任意距离上的径向畸变参数，以下为求任意不同距离上的径向畸变参数的方法。Since the radial distortion in the present invention is related to the object distance, it is necessary to calibrate the radial distortion parameters on two distances, and further solve the radial distortion parameters on other arbitrary distances. The following is to find the radial distortion on any different distances method with parameters.

步骤104：在两个不同距离上标定所述场相关畸变标定参数，即径向畸变参数，并推导得到任意其他距离上空间点在相机像面上的畸变参数；Step 104: Calibrate the field-related distortion calibration parameters at two different distances, that is, the radial distortion parameters, and derive the distortion parameters of the spatial point on the camera image plane at any other distance;

根据本发明的一个实施例，所述步骤104中径向畸变参数标定方法为：According to an embodiment of the present invention, the radial distortion parameter calibration method in step 104 is:

d1)设相机相面对焦于S距离，利用共面直线阵列场标定两个距离S₁和S2上的径向畸变参数，分别为以及 d1) Assuming that the camera phase plane focuses _on the distance S, use the coplanar linear array field to calibrate the radial distortion parameters at the two distances S1 and S2, which are respectively as well as

步骤c4)中获取了相机相面对焦于S而物点位于S₁时，像面上的径向畸变量，同理，对于相机像面对焦于S而物点位于距离S₂时，像面上的径向畸变量模型：In step c4), when the camera phase plane is focused on S and the object point is located at S1, the radial distortion _on the image plane is obtained. Similarly, when the camera image plane is focused _on S and the object point is located at a distance of S2, Radial distortion model on the image plane:

$\begin{matrix} {δ δ}_{{rss rss}_{22}} = = \frac{{C C}_{{s the s}_{22}}^{22}}{{C C}_{s the s}^{22}} {k k}_{11 {s the s}_{22}} {r r}_{s the s}^{33} + + \frac{{C C}_{{s the s}_{22}}^{44}}{{C C}_{s the s}^{44}} {k k}_{22 {s the s}_{22}} {r r}_{s the s}^{55} + + \frac{{C C}_{{s the s}_{22}}^{66}}{{C C}_{s the s}^{66}} {k k}_{33 {s the s}_{22}} {r r}_{s the s}^{77} \\ = = {k k}_{11 {ss ss}_{22}} {r r}_{s the s}^{33} + + {k k}_{22 {ss ss}_{22}} {r r}_{s the s}^{55} + + {k k}_{33 {ss ss}_{22}} {r r}_{s the s}^{77} \end{matrix}$

在实验环境下，可以通过建立特定的标定场来标定任意距离上相机像面上的径向畸变参数，即以及 In the experimental environment, the radial distortion parameters on the camera image plane at any distance can be calibrated by establishing a specific calibration field, namely as well as

d2)设已知镜头焦距f，在标定时测量同时记录下S₁和S₂的精确值，利用下述公式求取和 _d2 ) Assuming that the focal length f of the lens is known, measure and record the exact values _of S1 and S2 at the same time during calibration, and use the following formula to obtain and

$\frac{11}{{C C}_{{s the s}_{11}}} + + \frac{11}{{s the s}_{11}} = = \frac{11}{f f},, \frac{11}{{C C}_{{s the s}_{22}}} + + \frac{11}{{s the s}_{22}} = = \frac{11}{f f}$

d3)利用步骤103中的结论，由c4中的公式可以建立离焦状态下径向畸变参数的标定结果以及同对焦状态下的畸变参数以及之间的数学关系:d3) Using the conclusion in step 103, the calibration result of the radial distortion parameter in the out-of-focus state can be established by the formula in c4 as well as Distortion parameters in the same focus state as well as The mathematical relationship between:

$\frac{11}{{C C}_{s the s}^{22}} {k k}_{11 {s the s}_{11}} = = \frac{11}{{C C}_{{s the s}_{11}}^{22}} {k k}_{11 {ss ss}_{11}},, \frac{11}{{C C}_{s the s}^{22}} {k k}_{11 {s the s}_{22}} = = \frac{11}{{C C}_{{s the s}_{22}}^{22}} {k k}_{11 {ss ss}_{22}}$

$\frac{11}{{C C}_{s the s}^{44}} {k k}_{22 {s the s}_{11}} = = \frac{11}{{C C}_{{s the s}_{11}}^{44}} {k k}_{22 {ss ss}_{11}},, \frac{11}{{C C}_{s the s}^{44}} {k k}_{22 {s the s}_{22}} = = \frac{11}{{C C}_{{s the s}_{22}}^{44}} {k k}_{22 {ss ss}_{22}}$

$\frac{11}{{C C}_{s the s}^{66}} {k k}_{33 {s the s}_{11}} = = \frac{11}{{C C}_{{s the s}_{11}}^{66}} {k k}_{33 {ss ss}_{11}},, \frac{11}{{C C}_{s the s}^{66}} {k k}_{33 {s the s}_{22}} = = \frac{11}{{C C}_{{s the s}_{22}}^{66}} {k k}_{33 {ss ss}_{22}}$

d4)当已知对焦于两距离上的畸变参数和根据Brown的模型，由对焦状态下两个距离上的畸变参数，获取对焦于任意距离S′处的相机像面畸变量；d4) When the distortion parameters focusing on two distances are known and According to Brown's model, the image plane distortion of the camera focusing at any distance S' is obtained from the distortion parameters at two distances in the focusing state;

δ_rs′＝k_1s′r_s′ ³+k_2s′r_s′ ⁵+k_3s′r_s′ ⁷ δ _rs' = k _1s' r _s' ³ +k _2s' r _s' ⁵ +k _3s' r _s' ⁷

其中：in:

${k k}_{11 {s the s}^{' '}} = = {α α}_{{s the s}^{' '}} {k k}_{11 {s the s}_{11}} + + ((11 - - {α α}_{{s the s}^{' '}})) {k k}_{11 {s the s}_{22}}$

${k k}_{22 {s the s}^{' '}} = = {α α}_{{s the s}^{' '}} {k k}_{22 {s the s}_{11}} + + ((11 - - {α α}_{{s the s}^{' '}})) {k k}_{22 {s the s}_{22}}$

${k k}_{33 {s the s}^{' '}} = = {α α}_{{s the s}^{' '}} {k k}_{33 {s the s}_{11}} + + ((11 - - {α α}_{{s the s}^{' '}})) {k k}_{33 {s the s}_{22}}$

${α α}_{{s the s}^{' '}} = = \frac{{S S}_{22} - - {S S}^{' '}}{{S S}_{22} - - {S S}_{11}} \cdot &Center Dot; \frac{{S S}_{11} - - f f}{{S S}^{' '} - - f f}$

α_s′为可计算量。α _s' is a calculable quantity.

d5)再将畸变量δ_rs′离焦至相机像面上(主距为C_s)，得到：d5) Then defocus the distortion δ _rs′ to the camera image plane (principal distance is C _s ), and get:

δ_rss′＝γ_ss′ ²k_1s′r_s ³+γ_ss′ ⁴k_2s′r_s ⁵+γ_ss′ ⁶k_3s′r_s ⁷ δ _rss' = γ _ss' ² k _1s' r _s ³ + γ _ss' ⁴ k _2s' r _s ⁵ + γ _ss' ⁶ k _3s' r _s ⁷

＝k_1ss′r_s ³+k_2ss′r_s ⁵+k_3ss′r_s ⁷ =k _1ss′ r _s ³ +k _2ss′ r _s ⁵ +k _3ss′ r _s ⁷

其中：in:

${γ γ}_{{ss ss}^{' '}} = = \frac{{C C}_{{s the s}^{' '}}}{{C C}_{s the s}}$

C_s′为可计算量；C _s' is a calculable quantity;

${k k}_{11 {ss ss}^{' '}} = = {C C}_{{s the s}^{' '}}^{22} {α α}_{{s the s}^{' '}} \frac{11}{{C C}_{s the s}^{22}} {k k}_{11 {s the s}_{11}} + + {C C}_{{s the s}^{' '}}^{22} ((11 - - {α α}_{{s the s}^{' '}})) \frac{11}{{C C}_{s the s}^{22}} {k k}_{11 {s the s}_{22}}$

${k k}_{22 {ss ss}^{' '}} = = {C C}_{{s the s}^{' '}}^{44} {α α}_{{s the s}^{' '}} \frac{11}{{C C}_{s the s}^{44}} {k k}_{22 {s the s}_{11}} + + {C C}_{{s the s}^{' '}}^{44} ((11 - - {α α}_{{s the s}^{' '}})) \frac{11}{{C C}_{s the s}^{44}} {k k}_{22 {s the s}_{22}}$

${k k}_{33 {ss ss}^{' '}} = = {C C}_{{s the s}^{' '}}^{66} {α α}_{{s the s}^{' '}} \frac{11}{{C C}_{s the s}^{66}} {k k}_{33 {s the s}_{11}} + + {C C}_{{s the s}^{' '}}^{66} ((11 - - {α α}_{{s the s}^{' '}})) \frac{11}{{C C}_{s the s}^{66}} {k k}_{33 {s the s}_{22}}$

d7)计算物距在S′，并求得像面对焦于S距离时的径向畸变参数：d7) Calculate the object distance at S′, and obtain the radial distortion parameter when the image plane focuses on the S distance:

${k k}_{11 {ss ss}^{' '}} = = {α α}_{{s the s}^{' '}} \frac{{C C}_{{s the s}^{' '}}^{22}}{{C C}_{{s the s}_{11}}^{22}} {k k}_{11 {ss ss}_{11}} + + ((11 - - {α α}_{{s the s}^{' '}})) \frac{{C C}_{{s the s}^{' '}}^{22}}{{C C}_{{s the s}_{22}}^{22}} {k k}_{11 {ss ss}_{22}}$

${k k}_{22 {ss ss}^{' '}} = = {α α}_{{s the s}^{' '}} \frac{{C C}_{{s the s}^{' '}}^{44}}{{C C}_{{s the s}_{11}}^{44}} {k k}_{22 {ss ss}_{11}} + + ((11 - - {α α}_{{s the s}^{' '}})) \frac{{C C}_{{s the s}^{' '}}^{44}}{{C C}_{{s the s}_{22}}^{44}} {k k}_{22 {ss ss}_{22}}$

${k k}_{33 {ss ss}^{' '}} = = {α α}_{{s the s}^{' '}} \frac{{C C}_{{s the s}^{' '}}^{66}}{{C C}_{{s the s}_{11}}^{66}} {k k}_{33 {ss ss}_{11}} + + ((11 - - {α α}_{{s the s}^{' '}})) \frac{{C C}_{{s the s}^{' '}}^{66}}{{C C}_{{s the s}_{22}}^{66}} {k k}_{33 {ss ss}_{22}}$

步骤d7)表明，可以通过任意两距离S₁和S₂上的径向畸变参数标定结果，计算其他距离S′上的径向畸变参数。还表明，这种方法甚至不需要测量相机像面的对焦距离S或者C_s，进一步减少了标定工作量。Step d7) indicates that the radial distortion parameters at other distances S′ can be calculated by the calibration results of the radial distortion parameters at any two distances S ₁ and S ₂ . It is also shown that this method does not even need to measure the focus distance S or C _s of the camera image plane, which further reduces the calibration workload.

步骤105：利用步骤104中获取的径向畸变参数计算不同成像半径上的径向畸变量。Step 105: Using the radial distortion parameters acquired in step 104 to calculate the radial distortion at different imaging radii.

本发明通过以下实验验证本发明所述的摄影测量相机的场相关畸变标定方法。The present invention verifies the field-dependent distortion calibration method of the photogrammetry camera described in the present invention through the following experiments.

如图2所示为畸变参数标定场，其中布置若干共面回光反射直线。由于畸变的存在，直线阵列成像为具有一定规则的弯曲曲线阵列。通过复杂的非线性最小二乘平差方法，将曲线校正为直线的畸变参数就是成像系统的畸变参数。As shown in Figure 2, it is the distortion parameter calibration field, in which several coplanar light reflection straight lines are arranged. Due to the existence of distortion, the linear array is imaged as a curved array with certain rules. Through the complex nonlinear least squares adjustment method, the distortion parameters that correct the curve to a straight line are the distortion parameters of the imaging system.

首先，研究径向及偏心畸变随物距变化情况。First, the variation of radial and eccentric distortion with object distance is studied.

本实验采用的工业相机为AVT GE4900，它具有1600万像素分辨率的全画幅传感器，用于实验的有焦距为50mm及35mm的两只定焦全画幅镜头，而且分别对焦于某一未知距离。在不同距离上标定径向和偏心畸变参数，同时计算不同成像半径上的径向及偏心畸变量，结果如表1和表2所示。The industrial camera used in this experiment is AVT GE4900, which has a full-frame sensor with a resolution of 16 million pixels. There are two fixed-focus full-frame lenses with a focal length of 50mm and 35mm used in the experiment, and they focus on an unknown distance respectively. The radial and eccentric distortion parameters were calibrated at different distances, and the radial and eccentric distortions at different imaging radii were calculated at the same time. The results are shown in Table 1 and Table 2.

表1不同距离、半径上，50mm镜头径向畸变和偏心畸变的变化Table 1 Changes in radial distortion and eccentric distortion of 50mm lens at different distances and radii

表2不同距离、半径上，35mm镜头径向畸变和偏心畸变的变化Table 2 Changes in the radial distortion and decentering distortion of the 35mm lens at different distances and radii

从两只镜头的标定结果可以看出，径向畸变量随物距变化发生了不可忽视的改变量，而偏心畸变量却保持稳定，验证了对于两种畸变的理论分析。From the calibration results of the two lenses, it can be seen that the radial distortion has a non-negligible change with the object distance, while the eccentric distortion remains stable, which verifies the theoretical analysis of the two distortions.

然后，对上述两种畸变进行标定和计算方法验证Then, the calibration and calculation method verification of the above two distortions

利用两个距离上的标定结果计算其他距离上的畸变量，然后与本距离上畸变量的标定结果进行比较，结果如表3和表4所示。Use the calibration results at the two distances to calculate the distortion at other distances, and then compare it with the calibration results of the distortion at this distance. The results are shown in Table 3 and Table 4.

表3利用50mm镜头第2，3次的标定结果计算其他距离上的径向畸变量Table 3 Calculate the radial distortion at other distances using the second and third calibration results of the 50mm lens

表4利用35mm镜头第2，5次的标定结果计算其他距离上的径向畸变量Table 4 calculates the radial distortion at other distances using the 2nd and 5th calibration results of the 35mm lens

计算结果同标定结果之间的偏差绝大部分小于1微米，尤其对于35mm镜头的标定，从而验证了径向畸变标定方法的理论模型。作为比较，不考虑径向畸变量同物距之间的关系，直接利用某个距离上的标定结果计算其他距离的畸变量，同样与标定结果进行比较，结果如表5和表6所示。Most of the deviations between the calculated results and the calibration results are less than 1 micron, especially for the calibration of the 35mm lens, thus verifying the theoretical model of the radial distortion calibration method. As a comparison, regardless of the relationship between the radial distortion and the object distance, the calibration results at a certain distance are directly used to calculate the distortion at other distances, and the results are also compared with the calibration results. The results are shown in Table 5 and Table 6.

表5 50mm镜头不考虑物距影响时的径向畸变量及误差Table 5 Radial distortion and error of 50mm lens without considering the influence of object distance

表6 35mm镜头不考虑物距影响时的径向畸变量及误差Table 6 Radial distortion and error of 35mm lens without considering the influence of object distance

表5和表6的对比数据说明，当不考虑物距带来的径向畸变变化时，会产生较大的系统误差。考虑本发明中的物距-畸变模型后，此系统误差被极大减小。The comparative data in Table 5 and Table 6 shows that when the radial distortion change caused by the object distance is not considered, a large systematic error will occur. After considering the object distance-distortion model in the present invention, the systematic error is greatly reduced.

通过以上实验证明，本发明提出的离焦状态畸变模型中，径向畸变量随物距发生明显变化，偏心畸变量不发生改变；The above experiments prove that in the defocus state distortion model proposed by the present invention, the radial distortion varies significantly with the object distance, and the eccentric distortion does not change;

本发明提出的离焦状态下的标定模型和方法可以标定任意对焦距离的工业相机。这种方法适合于定主距的工业测量用相机，克服了对焦误差带来的影响，甚至不需要知道相机的对焦距离，极大提高了标定效率和后续测量精度；The calibration model and method in the out-of-focus state proposed by the invention can calibrate industrial cameras with arbitrary focus distances. This method is suitable for industrial measurement cameras with a fixed main distance, which overcomes the influence of focus errors, and does not even need to know the focus distance of the camera, which greatly improves the calibration efficiency and subsequent measurement accuracy;

本发明提出利用任意两个距离上的径向畸变标定结果，可计算任意其他距离上的径向畸变参数，利用任意一个距离上的偏心畸变标定结果，可以计算任意其他距离上的偏心畸变参数，计算结果误差非常小。The present invention proposes to use the radial distortion calibration results at any two distances to calculate the radial distortion parameters at any other distance, and to calculate the eccentric distortion parameters at any other distance by using the eccentric distortion calibration results at any one distance. The calculation result error is very small.

本发明克服了相机标定时对于对焦的依赖，简化了标定过程，不依赖准确的镜头焦距和物距测量，消除离焦带来的系统误差；标定相机完毕即可以固定相机主距，在后续测量中保证测量精度的稳定；模型非常适合于高精度三维测量工业相机的标定，对于在工业领域推广大尺寸的动态摄影测量技术具有理论和实践意义。The present invention overcomes the dependence on focus during camera calibration, simplifies the calibration process, does not rely on accurate lens focal length and object distance measurement, and eliminates the system error caused by defocus; after the camera is calibrated, the main distance of the camera can be fixed, and the subsequent measurement The stability of the measurement accuracy is guaranteed in the middle; the model is very suitable for the calibration of high-precision three-dimensional measurement industrial cameras, and has theoretical and practical significance for the promotion of large-scale dynamic photogrammetry technology in the industrial field.

以上只是本发明较佳的实例，并非来限制本发明实施范围，故凡依本发明申请专利范围所述的构造、特征及原理所做的等效变化或修饰，均应包括于本发明专利申请范围内。The above are only preferred examples of the present invention, and are not intended to limit the implementation scope of the present invention, so all equivalent changes or modifications made according to the structure, features and principles described in the scope of the patent application of the present invention should be included in the patent application of the present invention within range.

Claims

1. A field-dependent distortion calibration method for a photogrammetric camera is characterized by comprising the following steps:

a) establishing a return light reflection coplanar linear array field for calibrating field-related distortion;

b) adjusting the focusing state of a camera to be calibrated according to the requirements of the depth of field and the distance of a measuring environment, and fixing an imaging system of the camera to prevent the camera from focusing;

c) establishing a field-related radial distortion model in any focusing state;

d) calibrating field-related distortion calibration parameters, namely radial distortion parameters, at two different distances to obtain distortion parameters of space points at the image surface of the camera at any other distance;

e) and d, calculating the radial distortion quantity on different imaging radii by using the radial distortion parameters acquired in the step d.

2. The method for calibrating field dependent distortion as set forth in claim 1, wherein the step of establishing the field dependent distortion calibration field in step a) comprises:

a1) unfolding the frame, supporting a movable joint of the frame by using a connecting rod, and keeping the frame stable;

a2) fixing linear materials at the upper end and the lower end of the frame vertically in parallel, stretching the linear materials, and keeping the linearity of the linear materials;

a3) and the coding points are arranged on the connecting rod and used for measuring and adjusting the angle of the optical axis of the camera during calibration.

3. The method for calibrating field dependent distortion of claim 2, wherein: the frame is a stretching frame and can be contracted and expanded; the frame has a deployed dimension of at least 3 meters in length and 2 meters in height.

4. The method for calibrating field dependent distortion of claim 2, wherein: the background of the frame is arranged as black light absorbing lint for reducing imaging background noise from ambient light.

5. The method for calibrating field dependent distortion of claim 2, wherein: the linear material is arranged as a light return reflection line having a width determined by the distance of the camera from the calibration field when calibrating.

6. The method for calibrating field dependent distortion of claim 2, wherein: the reflecting material of the return light reflecting line is glass beads.

7. The method for calibrating field dependent distortion of claim 2, wherein: the stretching method of the linear material comprises the steps that G-shaped clamps are arranged at the upper end and the lower end of the frame, and the linear material is stretched through the G-shaped clamps.

8. The method for calibrating field dependent distortion of claim 1, wherein the method for establishing the radial distortion model in step c) comprises:

c1) setting a camera phase plane to focus at a distance S, and positioning a measured point on an object plane at a distance S1 from the camera to obtain a radial distortion;

c2) setting the camera to focus on S₁The radial distortion parameter of the focal plane at object distance isObtaining the radial distance on the image surface in the focusing state asThe amount of radial distortion at any image point of (a);

c3) then setting the image plane of the camera to focus at the distance S, and obtaining the S by utilizing the similarity analysis of the defocusing distortion₁Distortion of an object point on a distance plane on an actual image plane of the camera.

9. The method for calibrating field dependent distortion as set forth in claim 1, wherein the method for calibrating radial distortion parameters in step d) comprises:

d1) setting the camera phase plane to focus on the S distance, and calibrating the two distances S by using the coplanar linear array field₁And S₂The radial distortion parameter of (1) isAnd

d2) given a known lens focal length f, the distance S is recorded while measuring at the time of calibration₁And S₂To find the image distanceAnd

d3) c, establishing a calibration result of the radial distortion parameter in the defocusing state by using the conclusion in the step CAnddistortion parameter in-focus stateAnda mathematical relationship therebetween;

d4) according to the Brown model, the distortion quantity of the camera image surface focused at any distance S' is obtained according to the distortion parameters at two distances in the focusing state_rs′；

Wherein the relationship between the distortion parameter in focus at two distances and the corresponding defocus distortion parameter is known, described by d 3).

d5) Amount of distortion_rs′Defocusing to an image surface of the camera;

d6) calculating each radial distortion parameter:

d7) and calculating the object distance S' and obtaining the radial distortion parameter when the image plane focuses on the distance S.