A measurement method, device and control equipment based on a fringe projection measurement model

Abstract

The application provides a kind of measurement method, device and control equipment based on stripe projection measurement model, measurement method includes: based on three coordinate systems, the geometric relationship between camera, projector and measured point in stripe projection measurement model is used to establish the first mapping relationship between the depth coordinate of measured point under camera coordinate system and corresponding absolute phase value, obtain the mathematical expression of stripe projection measurement model;Three coordinate systems include world coordinate system, camera coordinate system and pixel coordinate system;The stripe projection measurement system is calibrated, and the parameters to be calibrated in the mathematical expression are determined;Wherein, stripe projection measurement system is constructed using stripe projection measurement model;According to the absolute phase value and pixel coordinate of measured point obtained by stripe projection measurement system, the three-dimensional coordinates of measured point are obtained.The scheme can solve the problem that the stripe projection measurement method based on phase height mapping in the prior art is too dependent on phase difference, reference plane and precision measuring tool.

Description

Technical Field

[0001] This invention relates to the field of optical measurement technology, and in particular to a measurement method, apparatus, and control device based on a fringe projection measurement model. Background Technology

[0002] The fringe projection measurement method, as a structured light three-dimensional measurement method, has the characteristics of fast measurement speed, high accuracy, stress-free contact, wide application range, and convenience. It is widely used in industrial measurement, reverse engineering, biomedicine, cultural relic restoration, and daily life and entertainment.

[0003] Fringe projection measurement requires projecting a series of sinusoidal fringe patterns with a certain phase difference onto the surface of the object being measured. Then, the fringe pattern, after being modulated and deformed by the object's surface, is acquired. The enveloping phase is calculated, and the absolute phase value of the object's surface is determined using a phase unfolding algorithm. Finally, the depth information of the object's surface is obtained based on the measurement system model to achieve three-dimensional measurement. Therefore, a typical fringe projection measurement system generally includes a camera, a projector, and a computer.

[0004] Since fringe projection measurement systems must be calibrated before 3D measurements can be performed, the calibration of the measurement system is closely related to the measurement results. Based on different measurement principles, measurement system calibration methods can be mainly divided into three categories: traditional fringe projection calibration methods based on geometric constraints, pseudo-camera calibration methods based on stereo vision principles, and fringe projection calibration methods based on phase-height mapping relationships.

[0005] The first category is the traditional fringe projection calibration method based on geometric constraints. This type of method establishes a model through the geometric structural parameters between the systems, and only requires calibration of these parameters to achieve 3D measurement. However, this method places strict requirements on the spatial relative positions of the camera, projector, and reference plane. For example, the line connecting the optical centers of the camera and projector needs to satisfy a parallel constraint with the reference plane, the optical axis of the camera or projector needs to satisfy a perpendicular constraint with the reference plane, and the optical axes of the camera and projector need to satisfy an intersection constraint on the reference plane. These parallel, perpendicular, and intersecting geometric constraints greatly reduce the flexibility and efficiency of the measurement system calibration, while also placing extremely high demands on the system's installation accuracy. Currently, some scholars have proposed improved fringe projection measurement models to relax the geometric constraints between the camera, projector, and reference plane, but these methods still cannot completely eliminate the aforementioned limitations of the measurement system.

[0006] The second category is the pseudo-camera method based on stereo vision principles. Similar to stereo vision measurement methods, this method requires simultaneous calibration of both the camera and projector before measurement to obtain their spatial relationship. Since camera calibration technology is very mature, the key technology of this measurement method lies in the calibration of the projector. This type of method is simple to operate because it does not require consideration of the spatial relationship between the camera and projector in practical use. However, the pseudo-camera method relies on phase values ​​to establish the correspondence between the camera and projector. The accuracy of the projector calibration results depends on the precision of the phase unfolding, and phase errors are unavoidable in actual calibration, affecting the projector calibration accuracy. Furthermore, the manufacturing precision of projector lenses is lower than that of industrial cameras; using a pinhole model during calibration will introduce calibration errors several times greater than those of cameras.

[0007] The third category is calibration methods for fringe projection measurement systems based on phase-height mapping. These methods establish a direct mathematical relationship between the phase values ​​of points on the object's surface and their height information using the least squares method, and then perform calibration measurements based on this phase-height mapping. This type of calibration method only needs to calibrate the correlation coefficient in the phase-height mapping, without needing to consider the parallel, perpendicular, or intersecting geometric constraints that the camera and projector must satisfy. However, existing calibration methods do not consider the impact of camera lens distortion on the measurement results during the measurement process, and the existence of a reference plane leads to error accumulation. Currently, although some scholars have proposed improved methods, problems such as high computational complexity, low computational efficiency, and time-consuming calculations still exist.

[0008] The idea behind fringe projection measurement methods based on phase-height mapping typically involves establishing a mathematical model of the measurement system. Under this model, the phase and height of the object's surface satisfy a certain correspondence, and solving this correspondence is key to phase-height mapping. Current methods use least squares fitting to calculate the calibration parameters of the measurement system. This method allows the camera and projector to completely escape the geometric constraints of traditional fringe projection measurement methods, enabling them to be placed anywhere in space. However, these methods also have their limitations: First, the phase value of the phase-height mapping relationship in most measurement models is the phase difference between the object and the reference plane, requiring the use of a reference plane. This inevitably leads to the accumulation of phase errors, which are then passed on to the object's height calculation. Furthermore, the reference plane reduces the efficiency of calibration and measurement to some extent. Second, the calibration process of most fringe projection measurement methods uses multiple parallel planes at known positions to perform least squares fitting on the parameters to be determined. Therefore, multiple precision gauge blocks or precision displacement stages are needed to move the reference plane to form multiple parallel planes.

[0009] In summary, traditional fringe projection measurement methods based on geometric constraints are limited by the geometric constraints of triangulation principles, making it difficult for cameras and projectors to meet stringent constraints during calibration. Pseudo-camera methods based on stereo vision principles have a simple structure, but projector calibration is affected by numerous factors affecting accuracy. Furthermore, fringe projection measurement methods based on phase-height mapping require reference planes, precision gauge blocks, or precision displacement stages for calibration to establish the mapping relationship between phase difference and height. This results in fringe projection measurement methods exhibiting drawbacks such as complex calibration and poor usability in practical applications. Summary of the Invention

[0010] This invention provides a measurement method, apparatus, and control device based on a fringe projection measurement model to solve the problem that the existing fringe projection measurement method based on phase height mapping is too dependent on phase difference, reference plane, and precision measuring instruments.

[0011] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0012] According to one aspect of the present invention, a measurement method based on a fringe projection measurement model is provided, comprising:

[0013] Based on three coordinate systems, the geometric relationship between the camera, projector, and measured point in the fringe projection measurement model is used to establish a first mapping relationship between the depth coordinates of the measured point in the camera coordinate system and the corresponding absolute phase value, thereby obtaining the mathematical expression of the fringe projection measurement model; wherein, the three coordinate systems include the world coordinate system, the camera coordinate system, and the pixel coordinate system; the measured point is a position point on the surface of the object to be measured;

[0014] The fringe projection measurement system is calibrated to determine the parameters to be calibrated in the mathematical expression; wherein the fringe projection measurement system is constructed using the fringe projection measurement model.

[0015] The three-dimensional coordinates of the measured point are obtained based on the absolute phase value and pixel coordinates of the measured point obtained by the fringe projection measurement system.

[0016] Optionally, based on three coordinate systems, and utilizing the geometric relationship between the camera, projector, and measured point in the fringe projection measurement model, a first mapping relationship is established between the depth coordinates of the measured point in the camera coordinate system and the corresponding absolute phase value, resulting in the mathematical expression of the fringe projection measurement model, including:

[0017] Based on the geometric relationship between the camera, projector and the measured point, a second mapping relationship between the Z-axis coordinate of the measured point in the world coordinate system and the corresponding absolute phase value is obtained.

[0018] Based on the pinhole imaging principle, the transformation relationship between the world coordinate system and the camera coordinate system, and the second mapping relationship, a third mapping relationship is obtained between the Z-axis coordinate of the measured point in the world coordinate system and the coordinate of the imaging point in the camera coordinate system; wherein, the imaging point is the imaging point of the measured point on the camera.

[0019] Based on the geometric relationship between the camera and the measured point, the transformation relationship between the camera coordinate system and the pixel coordinate system, and the third mapping relationship, a fourth mapping relationship is obtained between the Z-axis coordinate of the measured point in the camera coordinate system and the coordinate of the imaging point in the pixel coordinate system.

[0020] Based on the lens distortion effect formula and the fourth mapping relationship, the mathematical expression of the fringe projection measurement model is obtained.

[0021] Optionally, the formula for the effect of lens distortion is:

[0022]

[0023] Where u represents the x-coordinate of the pixel coordinate without lens distortion; v represents the y-coordinate of the pixel coordinate without lens distortion; u d The x-coordinate of the distorted pixel coordinates; v d The ordinate of the distorted pixel coordinates; s i,j and t i,j represents the distortion compensation coefficient; n represents the fitting order.

[0024] Optionally, the mathematical expression of the fringe projection measurement model is:

[0025]

[0026] Among them, Z C φ represents the Z-axis coordinate of the measured point in the camera coordinate system; n represents the fitting order, and n is a positive integer greater than or equal to 2; φ represents the absolute phase value of the measured point; a i,j b i,j c i,j and d i,j This indicates the parameter to be calibrated.

[0027] Optionally, obtaining the three-dimensional coordinates of the measured point based on the absolute phase value and pixel coordinates of the measured point obtained by the fringe projection measurement system includes:

[0028] Based on the Z-axis coordinates of the measured point in the camera coordinate system and the coordinate transformation formula, the three-dimensional coordinates of the measured point are calculated; wherein, the coordinate transformation formula is:

[0029]

[0030] Among them, u d The x-coordinate of the distorted pixel coordinates; v d Z represents the ordinate of the distorted pixel coordinates. C This indicates the Z-axis coordinate of the measured point in the camera coordinate system; This indicates the X-axis coordinate of the measured point in the camera coordinate system; This represents the Y-axis coordinate of the measured point in the camera coordinate system; f x f y u0 and v0 are different intrinsic parameters calibrated by the camera.

[0031] Optionally, calibrating the fringe projection measurement system and determining the parameters to be calibrated in the mathematical expression includes:

[0032] The projector projects a stripe pattern onto the calibration board, and the camera is controlled to capture an image of the calibration board; wherein the calibration board is located within the field of view of the camera and the projector;

[0033] Change the position of the calibration plate and repeat the above process until a preset number of images are acquired;

[0034] The image is processed to obtain first information of the sampling points on the calibration board; wherein, the first information includes pixel coordinates, absolute phase value and depth coordinates;

[0035] Based on the first information, the least squares method is used to iteratively optimize the N sampling points to determine the parameters to be calibrated.

[0036] Optionally, the stripe pattern is a sinusoidal stripe that satisfies the multi-frequency heterodyne requirement;

[0037] The step of processing the image to obtain the first information of the sampling points on the calibration board includes:

[0038] Based on the corner extraction method in image processing, the pixel coordinates of the sampling points are extracted; the multi-frequency heterodyne method is used to perform phase measurement and phase unwrapping operations, and bilinear interpolation is used to calculate the absolute phase value corresponding to the pixel coordinates of each sampling point;

[0039] Based on the camera calibration results, the depth coordinates of each sampling point are obtained.

[0040] According to another aspect of the present invention, a measuring device based on a fringe projection measurement model is provided, comprising:

[0041] The model building module is used to establish a first mapping relationship between the depth coordinates of the measured point in the camera coordinate system and the corresponding absolute phase value based on three coordinate systems and the geometric relationship between the camera, projector and the measured point in the fringe projection measurement model, thereby obtaining the mathematical expression of the fringe projection measurement model; wherein, the three coordinate systems include the world coordinate system, the camera coordinate system and the pixel coordinate system; the measured point is a position point on the surface of the object to be measured;

[0042] A parameter determination module is used to calibrate the fringe projection measurement system and determine the parameters to be calibrated in the mathematical expression; wherein the fringe projection measurement system is constructed using the fringe projection measurement model;

[0043] The coordinate calculation module is used to obtain the three-dimensional coordinates of the measured point based on the absolute phase value and pixel coordinates of the measured point obtained by the fringe projection measurement system.

[0044] According to another aspect of the present invention, a control device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor; when the processor executes the program, it implements the measurement method as described above.

[0045] The beneficial effects of this invention are:

[0046] The above scheme directly establishes the mapping relationship between the absolute phase value of the surface of the object under test and the spatial coordinates, without considering the geometric constraints between the camera and the projector. It can effectively overcome the strict requirements of traditional fringe projection measurement systems on the relative spatial positions of the camera, projector, and reference plane. Attached Figure Description

[0047] Figure 1 A flowchart illustrating the measurement method based on the fringe projection measurement model provided in an embodiment of the present invention;

[0048] Figure 2 This is a schematic diagram of one of the geometric models of the fringe projection measurement system provided in an embodiment of the present invention;

[0049] Figure 3 This is the second schematic diagram of the geometric model of the fringe projection measurement system provided in this embodiment of the invention.

[0050] Figure 4 This diagram illustrates the calibration process of the fringe projection measurement system provided in this embodiment of the invention.

[0051] Figure 5 This diagram illustrates the error distribution of distortion-free sampling point reconstruction provided in this embodiment of the invention.

[0052] Figure 6This is a schematic diagram illustrating the error distribution of distorted sampling point reconstruction provided in an embodiment of the present invention.

[0053] Figure 7 This is a schematic diagram showing the sampling point reconstruction error distribution when the fitting order n is 3, as provided in this embodiment of the invention.

[0054] Figure 8 This is a schematic diagram showing the sampling point reconstruction error distribution when the fitting order n is 4, as provided in this embodiment of the invention.

[0055] Figure 9 This is a schematic diagram showing the spatial distribution of the chessboard grid reconstructed when the fitting order n is 2, as provided in this embodiment of the invention.

[0056] Figure 10 This is a schematic diagram showing the feature point error distribution when the fitting order n is 2, as provided in this embodiment of the invention.

[0057] Figure 11 This is a schematic diagram showing the feature point error distribution when the fitting order n is 3, as provided in this embodiment of the invention.

[0058] Figure 12 This is a schematic diagram showing the feature point error distribution when the fitting order n is 4, as provided in this embodiment of the invention.

[0059] Figure 13 This is a schematic diagram of the horizontal and vertical straight lines to be measured on the checkerboard calibration plate provided in this embodiment of the invention;

[0060] Figure 14 This diagram illustrates the measurement error of the straight line AB provided in an embodiment of the present invention.

[0061] Figure 15 This diagram illustrates the linear CD measurement error provided in an embodiment of the present invention.

[0062] Figure 16 This is a schematic diagram showing the side length of the calibration board chessboard provided in this embodiment of the invention;

[0063] Figure 17 This is a schematic diagram showing the measurement results of the horizontal side length of the calibration board chessboard provided in this embodiment of the invention;

[0064] Figure 18 This is a schematic diagram showing the measurement results of the longitudinal side length of the calibration board chessboard provided in this embodiment of the invention;

[0065] Figure 19 This is a schematic diagram illustrating a measurement device based on a fringe projection measurement model provided in an embodiment of the present invention. Detailed Implementation

[0066] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0067] This invention addresses the problem that existing fringe projection measurement methods based on phase height mapping are overly dependent on phase difference, reference plane, and precision measuring instruments, by providing a measurement method, apparatus, and control device based on a fringe projection measurement model.

[0068] like Figure 1 As shown, one embodiment of the present invention provides a measurement method based on a fringe projection measurement model, comprising:

[0069] S11: Based on three coordinate systems, using the geometric relationship between the camera, projector and the measured point in the fringe projection measurement model, establish the first mapping relationship between the depth coordinates of the measured point in the camera coordinate system and the corresponding absolute phase value, and obtain the mathematical expression of the fringe projection measurement model.

[0070] The three coordinate systems include the world coordinate system, the camera coordinate system, and the pixel coordinate system; the measured point is a location point on the surface of the object to be measured.

[0071] In this embodiment, the camera and projector can be placed anywhere in the space, as long as the object to be measured is in the common area formed by the camera's measurement field and the projector's projection field.

[0072] It should be noted that the mathematical expression obtained in S11 includes parameters to be calibrated, which need to be determined through the calibration process.

[0073] S12: Calibrate the fringe projection measurement system to determine the parameters to be calibrated in the mathematical expression;

[0074] The fringe projection measurement system is constructed using the fringe projection measurement model.

[0075] In other words, by constructing a fringe projection measurement system using a fringe projection measurement model and then calibrating the fringe projection measurement system, the parameters to be calibrated can be determined.

[0076] S13: Obtain the three-dimensional coordinates of the measured point based on the absolute phase value and pixel coordinates of the measured point obtained by the fringe projection measurement system.

[0077] After steps S11 and S12, the mathematical expression for the complete fringe projection measurement model can be obtained. Then, using the fringe projection measurement system, the absolute phase value and pixel coordinates of the measured point can be obtained. Based on the obtained data and mathematical expression, the three-dimensional coordinates of the measured point can finally be obtained.

[0078] In this embodiment of the invention, the fringe projection measurement model can directly establish the mapping relationship between the absolute phase value of the surface of the object under test and the spatial coordinates, without considering the geometric constraints between the camera and the projector. This can effectively overcome the strict requirements of traditional fringe projection measurement systems on the spatial relative positions of the camera, projector, and reference plane.

[0079] Optionally, the step of establishing a first mapping relationship between the depth coordinates of the measured point in the camera coordinate system and the corresponding absolute phase value based on three coordinate systems and utilizing the geometric relationship between the camera, projector, and measured point in the fringe projection measurement model, thereby obtaining the mathematical expression of the fringe projection measurement model, may specifically include the following steps:

[0080] Step 1: Based on the geometric relationship between the camera, projector, and the measured point, obtain the second mapping relationship between the Z-axis coordinate of the measured point in the world coordinate system and the corresponding absolute phase value.

[0081] In an optional embodiment of the present invention, the fringe projection measurement model can be a single-camera fringe projection measurement system, comprising: an industrial camera, for example, a camera based on a charge-coupled device (CCD) chip; a projector, for example, a digital light processing (DLP) device; and a computer. The camera imaging plane is the CCD plane. Figure 2 The figure shows the geometric model of the fringe projection measurement system. In this geometric model, the camera and projector can be placed at any position in space, as long as the object to be measured is in the common area formed by the camera's measurement domain and the projector's projection domain.

[0082] The purpose of the fringe projection measurement model is to establish the relationship between the spatial coordinates of the measured point Q and its absolute phase. First, based on three coordinate systems, the fringe projection measurement model is described as follows:

[0083] like Figures 2 to 3 As shown, the three coordinate systems are: world coordinate system O W -X W Y W Z W Camera coordinate system O C -X C Y C Z C ;Pixel coordinate system o-uv on the imaging plane.

[0084] As an optional embodiment of the present invention, point O can be used. W By establishing a world coordinate system with the origin of the world coordinate system, the X-axis in this coordinate system can be represented as X. W The Y-axis is represented as YW The Z-axis is represented as Z w .

[0085] Among them, O P O W Indicates the projector's optical axis; point O P Located in plane X W O W Z W Inside, that is, the sinusoidal fringes projected by the projector and the Y... W Parallel to the axis; point O P′ Point O P In X W The projection point on the axis; θ represents O P O W With vertical axis Z w The included angle; L1 represents point O. P To plane X W O W Y W The distance.

[0086] In the camera coordinate system, O C Z C Indicates the camera's optical axis; point O C′ Point O C plane X in the world coordinate system W O W Y W The projection point on the surface; L2 represents point O. C To plane X W O W Y W The distance.

[0087] Point Q represents any point on the object to be measured; where point Q corresponds to point q on the CCD plane; O P The extension of Q intersects plane X. W O W Y W At point A; O C The extension of Q intersects plane X. W O W Y W Point B; point Q′ indicates that point Q lies on X. W O W Y W Projection points on the plane; points Q″ and O C″ A' and A' represent points Q' and O respectively. C′ A in X W The projection onto the plane; h represents the projection from point Q to plane X. W O W Y W The distance (i.e., the height of point Q).

[0088] It should be noted that the above geometric model is only used to illustrate one type of geometric model in the embodiments of the present invention. The setting of the three coordinate systems can also be represented by other forms, as long as the object to be measured is in the common area formed by the measurement domain of the camera and the projection domain of the projector. This effectively overcomes the strict requirements of the traditional fringe projection measurement system on the relative spatial positions of the camera, projector and reference plane, and can achieve efficient measurement.

[0089] Below, using the geometric relationships between the camera, projector, and measured point in three coordinate systems, we derive the basic expression for the height h of point Q:

[0090] according to The derivation yields the first formula, which can be expressed as:

[0091]

[0092] Similarly, according to The second formula can be derived, and it can be expressed as:

[0093]

[0094] Combining the first and second formulas, we can derive the third formula, which can be expressed as:

[0095]

[0096] The third formula is the basic expression for h. After obtaining this third formula, it is necessary to establish the relationship between h and the absolute phase. For example... Figure 3 As shown, the geometric relationship between the points can be represented by the fourth formula, which can be expressed as:

[0097]

[0098] Assume point O W If the fringe pitch at point A' is p0 and the fringe pitch at point A' is p, then the relationship between p0 and p satisfies the fifth formula, which can be expressed as:

[0099]

[0100] according to The sixth formula can be derived, and it can be expressed as:

[0101]

[0102] Since the phase at point Q is equal to the absolute phase at points A and A′, and φ represents the absolute phase, then φ satisfies the seventh formula, which can be expressed as:

[0103]

[0104] Where φ0 represents point O W The absolute phase at that point.

[0105] Combining the derivations of formulas four, five, six, and seven, we can obtain formula eight, which can be expressed as:

[0106]

[0107] Combining the third and eighth formulas, we obtain the ninth formula, which can be expressed as:

[0108]

[0109] Among them, coefficients C1~C4 and D1~D4 are related to The constant coefficients independent of φ, which are only related to the geometric parameters of the system, can be expressed by the following tenth formula:

[0110]

[0111] It should be noted that the ninth formula above represents the Z-axis coordinate of the measured point in the world coordinate system. The second mapping relationship between (i.e., height h) and the corresponding absolute phase value, that is, the relationship between height h and point B in X W coordinates on the axis And the relationship between the absolute phase φ of point Q on the object under test.

[0112] Step 2: Based on the pinhole imaging principle, the transformation relationship between the world coordinate system and the camera coordinate system, and the second mapping relationship, obtain the third mapping relationship between the Z-axis coordinate of the measured point in the world coordinate system and the coordinate of the imaging point in the camera coordinate system; wherein, the imaging point is the imaging point of the measured point on the camera.

[0113] In this step, the third mapping relationship can be derived based on the pinhole imaging principle. The specific process can be described as follows:

[0114] First, we need to establish the mathematical relationship between point B and point Q.

[0115] According to the principle of pinhole imaging, since points B and Q pass through point O... C Since they are on the same optical path, the corresponding points of points B and Q on the CCD imaging surface are the same point, namely point q.

[0116] Assume that the pixel coordinates of point q in the pixel coordinate system are (u,v), and the coordinates of point q in the camera coordinate system are... If f is the focal length of the camera, then points B and q satisfy the eleventh formula, which can be expressed as:

[0117]

[0118] Since point B satisfies the world coordinate system O W -X W Y W Z W To camera coordinate system O C -X C Y C Z C The rotation and translation transformations are used to derive the twelfth formula, which can be expressed as:

[0119]

[0120] Based on the eleventh and twelfth formulas, the thirteenth formula can be derived, which can be expressed as:

[0121]

[0122] Among them, the coefficients e1~e3 and f1~f3 are related to and Independent constant coefficients, which are only related to the intrinsic and extrinsic parameters of the camera calibration, can be represented by the following fourteenth formula:

[0123]

[0124] Combining equations 9, 13, and 14, we obtain equation 15, which can be expressed as:

[0125]

[0126] Among them, coefficients A1~A6 and B1~B6 are combinations of coefficients C1~C4 and D1~D4 with coefficients e1~e3 and f1~f3.

[0127] It should be noted that the above fifteenth formula represents the third mapping relationship between the Z-axis coordinate of the measured point in the world coordinate system and the coordinate of the imaging point in the pixel coordinate system, that is, the relationship between the height h of any point on the object to be measured and the corresponding coordinate of that point in the camera coordinate system.

[0128] Step 3: Based on the geometric relationship between the camera and the measured point, the transformation relationship between the camera coordinate system and the pixel coordinate system, and the third mapping relationship, obtain the fourth mapping relationship between the Z-axis coordinate of the measured point in the camera coordinate system and the coordinates of the imaging point in the pixel coordinate system.

[0129] In this step, since h is... For ease of calculation and expression, h is transformed into the camera coordinate system according to formula 15. Satisfying the sixteenth formula, the sixteenth formula can be expressed as:

[0130]

[0131] Combining formulas two and thirteen, we obtain formula seventeen, which can be expressed as:

[0132] Since the data obtained directly in the experiment is pixel coordinates, it can be... Represented by the corresponding point q(u,v) on the pixel plane. Furthermore, for ease of representation, the following will... Let it be Z C .but (u,v) satisfies the eighteenth formula, which can be expressed as:

[0133]

[0134] Among them, f x f y u0 and v0 are the intrinsic parameters calibrated by the camera.

[0135] Combining equations thirteen, fourteen, fifteen, and sixteen, we obtain equation nineteen, which can be expressed as:

[0136] Z C =[E1+E2φ+(E3+E4φ)u+(E5+E6φ)v+(E7+E8φ)u 2 +(E9+E 10 φ)v 2 +(E 11 +E 12 φ)uv] / [F1+F2φ+(F3+F4φ)u+(F5+F6φ)v+(F7+F8φ)u 2 +(F9+F 10 φ)v 2 +(F 11 +F 12 φ)uv]

[0137] Among them, E1~E 12 F1~F 12 These are constant coefficients independent of u, v, and φ.

[0138] It should be noted that the nineteenth formula above represents the fourth mapping relationship between the Z-axis coordinate of the measured point in the camera coordinate system and the coordinates of the imaging point in the pixel coordinate system. That is, without considering camera lens distortion, the mapping relationship between the spatial depth coordinates, pixel coordinates (coordinates in the pixel coordinate system), and phase value of any point on the object under test.

[0139] Step 4: Obtain the mathematical expression of the fringe projection measurement model based on the lens distortion effect formula and the fourth mapping relationship.

[0140] It should be noted that in practical applications, the influence of camera lens distortion on the measurement process needs to be considered. The relationship between the distorted pixel coordinates and the original pixel coordinates can be expressed by the twentieth formula, namely the lens distortion influence formula.

[0141] Optionally, the formula for the effect of lens distortion is:

[0142]

[0143] Where u represents the x-coordinate of the pixel coordinate without lens distortion; v represents the y-coordinate of the pixel coordinate without lens distortion; u d The x-coordinate of the distorted pixel coordinates; v d The ordinate of the distorted pixel coordinates; s i,j and t i,j represents the distortion compensation coefficient; n represents the fitting order.

[0144] It should be noted that u d v d This refers to data obtained directly from the image.

[0145] Combining formulas nineteen and twenty, we obtain formula twenty-one, which is the mathematical expression of the fringe projection measurement model. Optionally, the mathematical expression of the fringe projection measurement model is:

[0146]

[0147] Among them, Z C φ represents the Z-axis coordinate of the measured point in the camera coordinate system; n represents the fitting order, and n is a positive integer greater than or equal to 2; φ represents the absolute phase value of the measured point; a i,j b i,j c i,j and d i,j This indicates the parameter to be calibrated.

[0148] It should be noted that the above formula 21 can represent Z. C With the distorted pixel coordinates (u) of the lens distortion d ,vd The mapping relationship between the coefficient a and the absolute phase φ. i,j b i,j c i,j d i,j To be related to the distorted pixel coordinates (u d ,v d ) and an independent constant of the absolute phase value φ, a i,j b i,j c i,j d i,j It needs to be determined through calibration.

[0149] The fringe projection measurement model of this invention establishes a mapping relationship between the absolute phase value of the surface of the object to be measured and the spatial coordinates by combining the geometric relationship between the camera, projector and the object to be measured, and the principles of camera pinhole imaging and lens distortion model. This enables three-dimensional measurement of the surface of the object to be measured, and features simple structure, high measurement accuracy, fast measurement speed and ease of use.

[0150] Optionally, calibrating the fringe projection measurement system and determining the parameters to be calibrated in the mathematical expression includes:

[0151] (i) Projecting a stripe pattern onto a calibration plate using the projector and controlling the camera to capture an image of the calibration plate; wherein the calibration plate is located within the field of view of the camera and the projector.

[0152] (ii) Change the position of the calibration plate and repeat the above process until a preset number of images are acquired.

[0153] It should be noted that the preset number can be set according to the actual situation. For example, the preset number can be 19, which means that 19 sets of images (i.e., calibration images) can be used for calibration.

[0154] (iii) Process the image to obtain the first information of the sampling points on the calibration board; wherein the first information includes pixel coordinates, absolute phase value and depth coordinates.

[0155] Optionally, the stripe pattern is a sinusoidal stripe that satisfies the requirements of multi-frequency heterodyne; wherein, processing the image to obtain the first information of the sampling points on the calibration board includes: extracting the pixel coordinates of the sampling points based on a corner extraction method in image processing; performing phase measurement and phase unwrapping operations using a multi-frequency heterodyne method, and calculating the absolute phase value corresponding to the pixel coordinates of each sampling point using bilinear interpolation; and obtaining the depth coordinates of each sampling point based on the camera calibration results.

[0156] It should be noted that the sampling point is the point on the test object when the calibration plate is used as the test object.

[0157] This invention provides an embodiment of a three-dimensional fringe projection measurement system based on a fringe projection measurement model. The following section uses this fringe projection measurement system to verify the feasibility of the measurement method provided in this invention and the validity of the simulation results.

[0158] Specifically, in an optional embodiment of the present invention, the fringe projection measurement system can be a monocular fringe projection three-dimensional fringe projection measurement system. For example, it may include a CMOS monochrome camera with a maximum resolution of 2560×2048, a DMD projector with a resolution of 912×1140, a 12×9 black and white checkerboard calibration board with a checkerboard size of 15mm×15mm (±0.01mm), and a computer 401 (e.g., a computer with a main frequency of 3.7GHz).

[0159] like Figure 4 The diagram shown illustrates the calibration process of the fringe projection measurement system during the experiment.

[0160] In this embodiment, a multi-frequency heterodyne method is used for phase measurement and phase unfolding operations.

[0161] like Figure 4 As shown in step 1, three sinusoidal fringe patterns with fringe frequencies that meet the multi-frequency heterodyne requirement are designed by computer 401 and input into projector 403. The sinusoidal fringe frequencies are 1 / 70, 1 / 64 and 1 / 59 respectively. The phase shifting method is 4-step phase shifting. Therefore, a total of 12 sinusoidal fringe patterns are used.

[0162] Before the experiment begins, the sinusoidal stripe pattern 801 is burned into the ROM (Read-Only Memory) of the projector 403. The projector 403 can automatically project the stripe pattern and can be set to control the camera 404 to capture the pattern, thereby improving image acquisition efficiency.

[0163] like Figure 4 As shown in step 2, the calibration plate is placed within the field of view of the camera 404 and the projector 403, and the projector 403 projects a sinusoidal stripe pattern 801 onto the calibration plate.

[0164] like Figure 4 As shown in steps 3 and 4, firstly, keeping the position of the calibration plate unchanged, use camera 404 to capture images of the calibration plate and the striated image of the calibration plate after continuously projecting 12 fringe patterns. Then, change the position of the calibration plate and repeat step 2 until camera 404 captures enough calibration images (i.e., striated images corresponding to the calibration plate).

[0165] It should be noted that at least three sets of calibration images are required to complete the calibration process, while 10-20 sets of calibration images can usually achieve high calibration accuracy and meet the calibration requirements. In this embodiment of the invention, 19 sets of calibration images are used for calibration to obtain more accurate experimental results.

[0166] like Figure 4 As shown in step 5, the acquired calibration image is input into computer 401 for image processing operations such as filtering and denoising. For each location of the calibration image, operations such as extracting checkerboard calibration board feature points (i.e., sampling points), extracting the phase value of the feature points, and extracting the corresponding 3D coordinates of the feature points after calibration camera 404 are performed.

[0167] After the above process, the sub-pixel coordinates (u, v) of the feature points in the checkerboard calibration board image can be extracted, and the absolute phase value φ corresponding to the pixel coordinates of each feature point can be calculated using bilinear interpolation. Based on the camera 404 calibration results, the depth coordinate Z corresponding to each feature point can be obtained. C .

[0168] (iv) Based on the first information, the least squares method is used to iteratively optimize the N sampling points to determine the parameters to be calibrated.

[0169] It should be noted that after obtaining the pixel coordinates (u,v), absolute phase value φ, and depth coordinates Z... C Then, according to the twenty-first formula, least squares nonlinear parameter fitting can be performed to obtain the parameters required for system calibration (i.e., the parameters to be calibrated), thereby completing the system calibration.

[0170] The above calibration process involves collecting the absolute phase and spatial coordinates at feature points, combining them with the mathematical expression of the measurement model, and using the least squares method to solve for the system parameters, thereby achieving system calibration.

[0171] The calibration process in this embodiment can usually be completed in just 6 minutes. It is simple and convenient to operate, requires no reference plane, and avoids the introduction of error accumulation. It also does not require the use of high-precision auxiliary tools such as high-precision gauge blocks or precision displacement stages. Only a checkerboard calibration plate is needed to complete the system calibration. The camera lens distortion is taken into account, and the distortion model is combined to further improve the accuracy of the fringe projection measurement model.

[0172] It should be noted that the coefficient 'a' in formula 21... i,j b i,j c i,j d i,jThese represent constant coefficients related to system structure, camera intrinsic parameters, and extrinsic parameters. In practice, these parameters are difficult to measure precisely. Therefore, the Levenberg-Marquardt algorithm can be used to perform least-squares iterative optimization on N sampling points to achieve the desired parameter (a). i,j ,b i,j ,c i,j ,d i,j The exact fit of ) is obtained. The least squares bias can be expressed by the twenty-second formula, where the twenty-second formula is expressed as:

[0173]

[0174] Where N represents the number of sampling points; Z represents the spatial depth coordinates of the k-th sampling point; C The spatial depth coordinates are then obtained by calculating using the twenty-first formula.

[0175] Taking a fitting order of n=2 as an example, 24 system parameters need to be calibrated, and the equation formed by N sampling points can be expressed in matrix form as follows:

[0176] GH=0

[0177] in,

[0178]

[0179] H = [a 00 b 00 a 01 … b 20 c 00 d 00 c 01 … d 20 ]

[0180] Where G is an N×24 matrix and H is a 24×1 matrix.

[0181] The initial value of matrix H can be obtained through Singular Value Decomposition (SVD). After obtaining the initial value of matrix H, least squares optimization can be performed to obtain all the optimized parameters.

[0182] Optionally, obtaining the three-dimensional coordinates of the measured point based on the absolute phase value and pixel coordinates of the measured point obtained by the fringe projection measurement system includes:

[0183] Based on the Z-axis coordinates of the measured point in the camera coordinate system and the coordinate transformation formula (i.e., the twenty-sixth formula), the three-dimensional coordinates of the measured point are calculated; wherein, the coordinate transformation formula is:

[0184]

[0185] Among them, u d The x-coordinate of the distorted pixel coordinates; v d Z represents the ordinate of the distorted pixel coordinates. C This indicates the Z-axis coordinate of the measured point in the camera coordinate system; This indicates the X-axis coordinate of the measured point in the camera coordinate system; This represents the Y-axis coordinate of the measured point in the camera coordinate system; f x f y u0 and v0 are different intrinsic parameters calibrated by the camera.

[0186] Parameter to be calibrated (a) i,j ,b i,j ,c i,j ,d i,j The process of determining the coordinates is the system calibration process. After calibration, the absolute phase value and pixel coordinates obtained by the fringe projection measurement system can be substituted into formulas 21 and 26 to obtain the three-dimensional coordinates of the measured point, i.e., X. C Y C and Z C This enables convenient and quick 3D measurement and reconstruction.

[0187] In one embodiment of the present invention, the above-mentioned measurement method and fringe projection measurement model were analyzed by simulation, and the effectiveness of the fringe projection measurement model was verified by simulation and experimental results.

[0188] It should be noted that simulation calculations can eliminate various error interferences in the actual use of the fringe projection measurement system, such as manufacturing and assembly errors of the equipment itself, ambient light errors, nonlinearity errors of the projector, and phase measurement errors, etc. On the other hand, considering that various errors in actual experiments can interfere with the least squares fitting results, the results with or without distortion and with different fitting orders n may not have obvious distinguishability in actual use. Therefore, this paper uses simulation methods to verify the feasibility of the fringe projection measurement model, measurement method, and calibration, as well as the influence of different fitting orders n.

[0189] During the simulation, except for the absence of noise error, the calculation parameters used in the simulation are referenced from the real data, and the calculation method is consistent with that of the real data. The simulation process considers factors such as the presence or absence of camera lens distortion and the model fitting order, and analyzes the impact of these factors on the calibration and measurement results. The specific process is as follows:

[0190] The simulation area resolution was set to 800×640 pixels, and the equation of the simulated object under test was z=8×peaks(600). The system calibration used five randomly set planes with different postures, and equally spaced sampling points were selected on each plane to simulate the calibration plate used in the actual measurement.

[0191] Regarding the impact of camera lens distortion: When the camera lens has no distortion, the fitting order n in formula 21 is 2. To verify the magnitude of the impact of camera lens distortion on the measurement results, a set of control experiments was designed in the simulation experiment. The fitting order n of the measurement system was set to 2, and the system calibration and 3D measurement results were obtained for both cases with and without lens distortion. The distortion model is the one described in formula 20. The distortion parameters here refer to the distortion coefficients of an actual camera lens, and can be taken as follows: k1 = -0.021736, k2 = -0.80422, k3 = -0.00331, k4 = -0.00109, k5 = 0.

[0192] When the fitting order n is 2, the simulation results of the measurement error with and without lens distortion are as follows: Figure 5-6 As shown, where: Figure 5 As shown, this is the distribution of reconstruction error for distortion-free sampling points; Figure 6 The figure shows the reconstruction error distribution of distorted sampling points. Furthermore, the experiment can also obtain the reconstruction error of the undistorted object and the reconstruction error of the distorted object (not shown in the figure).

[0193] The calibration error distribution range of the simulation results without camera lens distortion is -2.5 × 10⁻⁶. -7 ~2.5×10 -7 Between mm, the error due to camera lens distortion is -2.5 × 10⁻⁶. -2 ~2.5×10 -2 The error ranges from 10 mm. Furthermore, the distortion-free 3D measurement and reconstruction error is within 10 mm. -6 The order of magnitude, with errors of 10 when distortion occurs. -2 The magnitude is significant. Therefore, it is evident that camera lens distortion has a substantial impact on the accuracy of the system's 3D measurements. To further improve the measurement accuracy of the fringe projection measurement system, the influence of lens distortion needs to be considered.

[0194] Regarding the influence of the model fitting order n: Simulations have demonstrated that camera lens distortion can cause significant errors in the measurement results. To minimize these errors, a fringe projection measurement system that considers the influence of camera lens distortion is required; that is, the fitting order n in formula 21 must be greater than 2. For example, simulation experiments were conducted with fitting orders n of 3 and 4, where the number of parameters to be calibrated for n of 2, 3, and 4 are 24, 40, and 60, respectively.

[0195] The experimental results (i.e., the simulation results of measurement error when the system fitting order n is 3 and 4 respectively) are as follows: Figure 7-8 As shown, where: Figure 7 The figure shows the sampling point reconstruction error distribution when n=3; as shown Figure 8 The figure shows the reconstruction error distribution of sampling points when n=4. Furthermore, the experiment can also obtain the reconstruction error of the object under test when n=3 and when n=4 (not shown in the figure).

[0196] The reconstruction error for n=3 is within 10. -3 The order of magnitude, with n=4, results in an error of 10. -6 The magnitude of the error distribution is shown in the experimental results. As the fitting order n increases, both the sampling point reconstruction error distribution and the object reconstruction error decrease continuously, and the error at n=4 is close to the reconstruction error under distortion-free conditions.

[0197] Analysis of calibration results: The calibration results of the fringe projection measurement system are as follows: Figure 10-12 As shown. Wherein:

[0198] like Figure 9 As shown, the spatial distribution of the chessboard reconstructed when the fitting order n=2 is obtained. This spatial distribution is calculated based on the parameters obtained from system calibration, combined with the extracted feature point pixel coordinates and absolute phase values. The spatial coordinates of the chessboard feature points obtained from camera calibration are used as the true values ​​for comparison and error analysis.

[0199] like Figure 10 , Figure 11 and Figure 12 The figures show the feature point error distributions for fitting orders n of 2, 3, and 4. The horizontal axis represents the range of error distribution, and the vertical axis represents the number of feature points within that range. Analysis of the data in the figures shows that as the fitting order n increases, the range of error distribution decreases, the error distribution becomes more concentrated, and the number of points close to zero increases significantly.

[0200] The root mean square error (RMSE, unit: mm) of the feature point reconstruction results of the checkerboard calibration board is shown in the table below:

[0201]

[0202]

[0203] From the root mean square error (RMSE) of the feature point reconstruction results of the checkerboard calibration board, we can intuitively see how the error changes with the fitting order; as n increases, the RMS error decreases. Simulation and experimental results verify that the fringe projection measurement model at order 4 achieves good measurement accuracy and can realize high-precision measurement on various complex surfaces. Therefore, considering both the measurement effect and the number of calibration parameters, subsequent calculations will use an order 4 fitting.

[0204] To further evaluate the measurement and reconstruction results, this embodiment of the invention performed 19 measurements on the lengths of the horizontal and vertical straight lines on the calibration plate at different locations in space. The measured straight lines are divided into two lines, horizontal and vertical, as follows: Figure 13 As shown, the horizontal line is a straight line AB with a length of 150 mm, and the vertical line is a straight line CD with a length of 105 mm. Three measurement methods were used: the measurement method provided in this embodiment of the invention (denoted as method a), the existing fourth-order polynomial measurement method (denoted as method b), and the classical phase-height mapping measurement method (denoted as method c). The accuracy of the measurement method provided in this embodiment of the invention was compared and verified. The fourth-order polynomial measurement method, employing polynomial fitting, can achieve relatively high measurement accuracy.

[0205] like Figure 13 As shown, the measurement errors of the horizontal and vertical straight lines to be measured on the checkerboard calibration board, lines AB and CD, under the three measurement methods are as follows: Figure 14 , 15 As shown: Among them, such as Figure 14 As shown, the measurement error of line AB is as follows: Figure 15 As shown, the measurement error of the straight line CD.

[0206] As can be seen, the measurement error range of the two straight lines measured by the measurement method provided in this embodiment of the invention and the fourth-order polynomial measurement method is both between -0.05mm and 0.05mm, while the error of the classical phase-height mapping measurement method is between -0.125mm and -0.175mm. Therefore, the measurement method provided in this embodiment of the invention has comparable accuracy to the fourth-order polynomial method and is superior to the classical phase-height mapping measurement method, achieving higher measurement accuracy.

[0207] Measurement Result Analysis: Error assessment was performed on the measurement of the side lengths of the square blocks in the checkerboard pattern. For example... Figure 16 The diagram shown is a schematic of the side length of the chessboard grid on the calibration board. The measurement process involves... Figure 16 The side lengths of all square checkerboard squares within the frame 1601 area were measured, and the horizontal and vertical side lengths were reconstructed and statistically analyzed. The horizontal and vertical side lengths are shown below. Figure 16As indicated by the labels, the measurement process involved measuring the lengths of all horizontal and vertical sides. The selected area had 80 horizontal sides (1603) and 77 vertical sides (1604).

[0208] The measurement results of the chessboard grid side length are as follows Figure 17-18 As shown, where: Figure 17 This is the result of the lateral side length measurement. Figure 18 The results show the longitudinal side length measurement. The results indicate that the measurement error is within ±0.035 mm.

[0209] The second set of experiments verified the accuracy of the fringe projection measurement system by measuring a custom-made ceramic standard sphere (diameter: 30mm ± 0.003mm). The point cloud data obtained was processed and analyzed using the reverse engineering software Geomagic Studio. The ceramic standard sphere measurement yielded the following results: the original image of the ceramic standard sphere, the fringe modulation map after projecting fringes onto the standard sphere, the absolute phase map corresponding to the fringe map, and the 3D reconstructed point cloud map of the measured standard sphere region.

[0210] For subsequent fitting calculations, the 3D reconstructed point cloud image of the aforementioned standard sphere region is processed, retaining only the 3D reconstructed point cloud of the standard sphere, resulting in an image with only the 3D reconstructed point cloud of the standard sphere. To demonstrate the stability and reliability of the fitting results, three different point cloud regions and point cloud numbers are used for sphere fitting, yielding three different result deviations. The specific fitting results (i.e., the fitting results of the 3D reconstructed point cloud of the standard sphere) are shown in the table below:

[0211]

[0212] As can be seen from the table, the error distribution is consistent with the error distribution range of the calibration results above, indicating that the measurement accuracy is stable and reliable.

[0213] Furthermore, to verify the effectiveness of the fringe projection measurement system for measuring complex 3D object surfaces, a complex 3D object surface measurement and reconstruction experiment can be conducted. Specifically, the surface of a 3D-printed complex object can be measured and reconstructed, with a measurement calculation time of 1.21 seconds. The object being measured is made of PLA plastic, with a complex surface shape, numerous discontinuous surfaces, and many details. By acquiring fringe images and calculating absolute phase images of the object, and then reconstructing point clouds of the object's surface, the original object image, fringe image, absolute phase image, and reconstructed point cloud of the object's surface can be obtained, respectively.

[0214] The reconstruction results show that the measurement method provided by the embodiments of the present invention can effectively achieve accurate measurement of the object surface and clearly present the detailed features of the object surface, with good three-dimensional measurement and reconstruction effect.

[0215] In this embodiment of the invention, the mapping relationship between the absolute phase value of the surface of the object to be measured and the spatial coordinates can be directly established without considering the spatial position relationship between the camera and the projector. The measurement process is simple and the measurement efficiency is high. No reference plane is required for the measurement, and the influence of camera lens distortion is considered, which improves the measurement accuracy of the measurement method. No precision measuring tools such as precision gauge blocks or precision displacement stages are required. The structure is simple, easy to use, and highly robust.

[0216] like Figure 19 As shown, this embodiment of the invention also provides a measuring device based on a fringe projection measurement model, comprising:

[0217] The model building module 190 is used to establish a first mapping relationship between the depth coordinates of the measured point in the camera coordinate system and the corresponding absolute phase value based on three coordinate systems and the geometric relationship between the camera, projector and the measured point in the fringe projection measurement model, thereby obtaining the mathematical expression of the fringe projection measurement model; wherein, the three coordinate systems include the world coordinate system, the camera coordinate system and the pixel coordinate system; the measured point is a position point on the surface of the object to be measured;

[0218] The parameter determination module 191 is used to calibrate the fringe projection measurement system and determine the parameters to be calibrated in the mathematical expression; wherein the fringe projection measurement system is constructed using the fringe projection measurement model;

[0219] The coordinate calculation module 192 is used to obtain the three-dimensional coordinates of the measured point based on the absolute phase value and pixel coordinates of the measured point obtained by the fringe projection measurement system.

[0220] The embodiments of the present invention can directly establish the mapping relationship between the absolute phase value of the surface of the object to be measured and the spatial coordinates, without considering the geometric constraints between the camera and the projector, and can effectively overcome the strict requirements of the traditional fringe projection measurement system on the spatial relative positions of the camera, projector and reference plane.

[0221] Optionally, the model building module 190 includes:

[0222] The first processing submodule is used to obtain a second mapping relationship between the Z-axis coordinate of the measured point in the world coordinate system and the corresponding absolute phase value, based on the geometric relationship between the camera, the projector and the measured point.

[0223] The second processing submodule is used to obtain a third mapping relationship between the Z-axis coordinates of the measured point in the world coordinate system and the coordinates of the imaging point in the camera coordinate system, based on the pinhole imaging principle, the transformation relationship between the world coordinate system and the camera coordinate system, and the second mapping relationship; wherein, the imaging point is the imaging point of the measured point on the camera.

[0224] The third processing submodule is used to obtain a fourth mapping relationship between the Z-axis coordinate of the measured point in the camera coordinate system and the coordinate of the imaging point in the pixel coordinate system, based on the geometric relationship between the camera and the measured point, the transformation relationship between the camera coordinate system and the pixel coordinate system and the third mapping relationship.

[0225] The fourth processing submodule is used to obtain the mathematical expression of the fringe projection measurement model based on the lens distortion influence formula and the fourth mapping relationship.

[0226] Optionally, the formula for the effect of lens distortion is:

[0227]

[0228] Where u represents the x-coordinate of the pixel coordinate without lens distortion; v represents the y-coordinate of the pixel coordinate without lens distortion; u d The x-coordinate of the distorted pixel coordinates; v d The ordinate of the distorted pixel coordinates; s i,j and t i,j represents the distortion compensation coefficient; n represents the fitting order.

[0229] Optionally, the mathematical expression of the fringe projection measurement model is:

[0230]

[0231] Among them, Z C φ represents the Z-axis coordinate of the measured point in the camera coordinate system; n represents the fitting order, and n is a positive integer greater than or equal to 2; φ represents the absolute phase value of the measured point; a i,j b i,j c i,j and d i,j This indicates the parameter to be calibrated.

[0232] Optionally, the coordinate calculation module 192 includes:

[0233] The coordinate calculation submodule is used to calculate the three-dimensional coordinates of the measured point based on the Z-axis coordinates of the measured point in the camera coordinate system and the coordinate transformation formula; wherein, the coordinate transformation formula is:

[0234]

[0235] Among them, u d The x-coordinate of the distorted pixel coordinates; v d Z represents the ordinate of the distorted pixel coordinates. C This indicates the Z-axis coordinate of the measured point in the camera coordinate system; This indicates the X-axis coordinate of the measured point in the camera coordinate system; This represents the Y-axis coordinate of the measured point in the camera coordinate system; f x f y u0 and v0 are different intrinsic parameters calibrated by the camera.

[0236] Optionally, the parameter determination module 191 includes:

[0237] The first calibration submodule is used to project a stripe pattern onto a calibration board using the projector and to control the camera to acquire an image of the calibration board; wherein the calibration board is located within the field of view of the camera and the projector;

[0238] The second calibration submodule is used to change the position of the calibration plate and repeat the above process until a preset number of images are acquired.

[0239] The third calibration submodule is used to process the image to obtain the first information of the sampling points on the calibration board; wherein, the first information includes pixel coordinates, absolute phase value and depth coordinates;

[0240] The fourth calibration submodule is used to determine the calibration parameters by iteratively optimizing N sampling points using the least squares method based on the first information.

[0241] Optionally, the stripe pattern is a sinusoidal stripe that satisfies the multi-frequency heterodyne requirement; wherein, the third calibration submodule includes:

[0242] The first calibration unit extracts the pixel coordinates of the sampling points based on the corner extraction method in image processing;

[0243] The second calibration unit uses a multi-frequency heterodyne method to perform phase measurement and phase unrolling operations, and uses bilinear interpolation to calculate the absolute phase value corresponding to the pixel coordinates of each sampling point.

[0244] The third calibration unit is used to obtain the depth coordinates of each sampling point based on the camera calibration results.

[0245] In this embodiment of the invention, the mapping relationship between the absolute phase value of the surface of the object to be measured and the spatial coordinates can be directly established without considering the spatial position relationship between the camera and the projector. The measurement process is simple and the measurement efficiency is high. No reference plane is required for the measurement, and the influence of camera lens distortion is considered, which improves the measurement accuracy of the measurement method. No precision measuring tools such as precision gauge blocks or precision displacement stages are required. The structure is simple, easy to use, and highly robust.

[0246] This invention also provides a control device, including a memory, a processor, and a computer program stored in the memory and executable on the processor; when the processor executes the program, it implements the measurement method described above.

[0247] The above describes the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications are also within the scope of protection of the present invention.

Claims

1. A measurement method based on a fringe projection measurement model, characterized in that, include: Based on three coordinate systems, the geometric relationship between the camera, projector, and measured point in the fringe projection measurement model is used to establish a first mapping relationship between the depth coordinates of the measured point in the camera coordinate system and the corresponding absolute phase value, thereby obtaining the mathematical expression of the fringe projection measurement model; wherein, the three coordinate systems include the world coordinate system, the camera coordinate system, and the pixel coordinate system; the measured point is a position point on the surface of the object to be measured; The fringe projection measurement system is calibrated to determine the parameters to be calibrated in the mathematical expression; wherein the fringe projection measurement system is constructed using the fringe projection measurement model. The three-dimensional coordinates of the measured point are obtained based on the absolute phase value and pixel coordinates of the measured point obtained by the fringe projection measurement system. Specifically, based on three coordinate systems, the geometric relationship between the camera, projector, and measured point in the fringe projection measurement model is used to establish a first mapping relationship between the depth coordinates of the measured point in the camera coordinate system and the corresponding absolute phase value, thereby obtaining the mathematical expression of the fringe projection measurement model, including: Based on the geometric relationship between the camera, projector, and the measured point, the measured point in the world coordinate system is obtained. Z The second mapping relationship between axis coordinates and their corresponding absolute phase values; Based on the pinhole imaging principle, the transformation relationship between the world coordinate system and the camera coordinate system, and the second mapping relationship, the measured point is obtained in the world coordinate system. Z A third mapping relationship between the axis coordinates and the coordinates of the imaging point in the camera coordinate system; wherein, the imaging point is the imaging point of the measured point on the camera; Based on the geometric relationship between the camera and the measured point, the transformation relationship between the camera coordinate system and the pixel coordinate system, and the third mapping relationship, a fourth mapping relationship is obtained between the Z-axis coordinate of the measured point in the camera coordinate system and the coordinate of the imaging point in the pixel coordinate system. Based on the lens distortion effect formula and the fourth mapping relationship, the mathematical expression of the fringe projection measurement model is obtained.

2. The measurement method according to claim 1, characterized in that, The formula for the influence of lens distortion is: ； in, The x-coordinate represents the pixel coordinates without the influence of lens distortion; The ordinate represents the pixel coordinates without lens distortion. The x-coordinate of the distorted pixel coordinates; The ordinate represents the distorted pixel coordinates; , , , , , , , , , , , , and Indicates the distortion compensation coefficient; This indicates the fitting order.

3. The measurement method according to claim 2, characterized in that, The mathematical expression for the fringe projection measurement model is: ； in, Indicates the measured point in the camera coordinate system Z Axis coordinates; n This indicates the fitting order, and n It is a positive integer greater than or equal to 2; This represents the absolute phase value of the measured point; , , and This indicates the parameter to be calibrated.

4. The measurement method according to claim 2, characterized in that, The step of obtaining the three-dimensional coordinates of the measured point based on the absolute phase value and pixel coordinates of the measured point obtained from the fringe projection measurement system includes: Based on the Z-axis coordinates of the measured point in the camera coordinate system and the coordinate transformation formula, the three-dimensional coordinates of the measured point are calculated; wherein, the coordinate transformation formula is: ； in, The x-coordinate of the distorted pixel coordinates; The ordinate represents the distorted pixel coordinates; This indicates the Z-axis coordinate of the measured point in the camera coordinate system; Indicates the measured point in the camera coordinate system X Axis coordinates; Indicates the measured point in the camera coordinate system Y Axis coordinates; , , , Different internal parameters are calibrated for the camera.

5. The measurement method according to claim 1, characterized in that, The calibration of the fringe projection measurement system, which determines the parameters to be calibrated in the mathematical expression, includes: The projector projects a stripe pattern onto the calibration board, and the camera is controlled to capture an image of the calibration board; wherein the calibration board is located within the field of view of the camera and the projector; Change the position of the calibration plate and repeat the above process until a preset number of images are acquired; The image is processed to obtain first information of the sampling points on the calibration board; wherein, the first information includes pixel coordinates, absolute phase value and depth coordinates; Based on the first information, the least squares method is used to... N The parameters to be calibrated are determined by iterative optimization at each sampling point.

6. The measurement method according to claim 5, characterized in that, The stripe pattern is a sinusoidal stripe that meets the requirements of multi-frequency heterodyne. The step of processing the image to obtain the first information of the sampling points on the calibration board includes: Based on the corner extraction method in image processing, the pixel coordinates of the sampling points are extracted; A multi-frequency heterodyne method is used to perform phase measurement and phase unrolling operations, and bilinear interpolation is used to calculate the absolute phase value corresponding to the pixel coordinates of each sampling point. Based on the camera calibration results, the depth coordinates of each sampling point are obtained.

7. A measuring device based on a fringe projection measurement model, characterized in that, include: The model building module is used to establish a first mapping relationship between the depth coordinates of the measured point in the camera coordinate system and the corresponding absolute phase value based on three coordinate systems and the geometric relationship between the camera, projector and the measured point in the fringe projection measurement model, thereby obtaining the mathematical expression of the fringe projection measurement model; wherein, the three coordinate systems include the world coordinate system, the camera coordinate system and the pixel coordinate system; the measured point is a position point on the surface of the object to be measured; A parameter determination module is used to calibrate the fringe projection measurement system and determine the parameters to be calibrated in the mathematical expression; wherein the fringe projection measurement system is constructed using the fringe projection measurement model; The coordinate calculation module is used to obtain the three-dimensional coordinates of the measured point based on the absolute phase value and pixel coordinates of the measured point obtained by the fringe projection measurement system. The model building module includes: The first processing submodule is used to obtain the measured point in the world coordinate system based on the geometric relationship between the camera, projector, and the measured point. Z The second mapping relationship between axis coordinates and their corresponding absolute phase values; The second processing submodule is used to obtain the measured point in the world coordinate system based on the pinhole imaging principle, the transformation relationship between the world coordinate system and the camera coordinate system, and the second mapping relationship. Z A third mapping relationship between the axis coordinates and the coordinates of the imaging point in the camera coordinate system; wherein, the imaging point is the imaging point of the measured point on the camera; The third processing submodule is used to obtain the measured point in the camera coordinate system based on the geometric relationship between the camera and the measured point, the transformation relationship between the camera coordinate system and the pixel coordinate system, and the third mapping relationship. Z A fourth mapping relationship between the axis coordinates and the coordinates of the imaging point in the pixel coordinate system; The fourth processing submodule is used to obtain the mathematical expression of the fringe projection measurement model based on the lens distortion influence formula and the fourth mapping relationship.

8. A control device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor; characterized in that, When the processor executes the program, it implements the measurement method as described in any one of claims 1 to 6.

Images