Image distortion correction system and method for flow field in transparent structure based on affine and b-spline grid transformation

Abstract

The application provides a transparent structure flow field image distortion correction system and method based on affine and B-spline grid transformation, which comprises a calibration paper, a structure outer sleeve box, a PIV system and a post-processing algorithm. The calibration paper is built in the structure and needs to cover the measured plane, and the distorted image can be directly observed; the structure outer sleeve water-tight box covers the measured structure, the box is filled with the solution in the structure, the observation window observed from the outside of the box is a plane, and the observed image distortion condition has been basically corrected; the PIV system comprises two high-speed cameras, a laser, a synchronizer and a computer; the polynomial mapping relationship of the images before and after the distortion is obtained through the post-processing software, the mapping relationship is reversely applied to the flow image inside the structure under the direct shooting condition, and the real flow condition without the distortion is obtained. The orthodontic effect is verified through the PIV test data of the flow field in the pipeline, and data support can be provided for the processing and analysis of the subsequent flow field test data in the complex structure.

Description

Technical Field

[0001] This invention belongs to the field of fluid mechanics experimental technology, specifically relating to an optical measurement system and method for the flow field inside a transparent structure by affine and B-spline mesh transformation. Background Technology

[0002] When measuring flow within a structure, experiments can be conducted through a transparent structural model. However, due to the difference in refractive index between the structure and water, the particle images captured by the camera will be distorted due to this refraction, leading to errors in the test results. Matching the refractive indices of the solid and liquid phases through solution mixing is not suitable for large-scale aquatic environments. Correcting the distortion errors in images when studying fluid motion characteristics within transparent structures will be an important approach to solving flow field tests within more complex structures. Distortion correction methods can provide data support for the subsequent processing and analysis of flow field test data within complex structures. Particle image velocimetry (PIV) is a flow field measurement technique that visualizes fluids, developed in the 1980s. With the rapid advancements in computer technology, optoelectronic technology, image processing technology, and other disciplines, PIV technology, as a multi-point, non-contact, and transient flow field measurement method, has gained popularity. Applying PIV technology to pipe flow research can not only improve measurement accuracy but also provide a more precise characterization of flow field features.

[0003] The orthogonalization method based on affine and B-spline mesh transformation is a non-rigid image registration method. Affine transformation refers to a global linear transformation of an image through a combination of translation, rotation, and scaling. The B-spline mesh-based image registration method controls the local transformation of the input image by constructing a B-spline control point mesh. A series of functions are generated using the hierarchical structure of the control point mesh. By applying B-spline thinning, the sum of these functions is equivalent to a B-spline function that produces a smooth, continuous transformation. Specifically, a set of characteristic coordinate points, called control points, can be determined in the calibration board images before and after the obstruction of the structure. Based on the B-spline transformation, the control points in the distorted image are mapped to the corresponding points in the undistorted image, providing a smooth transformation displacement field between the control points. Based on the motion displacement values ​​of the control points, an optimization algorithm is used to fit the motion displacement of each point in the image.

[0004] Most image optical distortion corrections target the optical components of imaging systems. This invention, however, targets the flow field or field of view itself, and uses post-processing techniques based on geometric optics to correct optical distortion in the raw PIV measurement data. Summary of the Invention

[0005] The purpose of this invention is to provide a system and method for correcting image distortion of the flow field inside a transparent structure based on affine and B-spline mesh transformation.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A distortion correction system for flow field images inside a transparent structure based on affine and B-spline mesh transformation includes calibration paper, a transparent structure, an outer casing for the structure, a PIV system, and a post-processing algorithm. The calibration paper is embedded in the transparent structure and covers the plane to be measured. The outer casing covers the transparent structure and is filled with a solution inside the structure. The PIV system includes a first high-speed camera, a second high-speed camera, a synchronizer, a laser, and a computer, all connected to the synchronizer. The post-processing algorithm obtains the polynomial mapping relationship of image points before and after distortion using post-processing software, and applies this mapping relationship inversely to the flow image inside the structure under direct shooting conditions to obtain the true flow situation without distortion.

[0008] Furthermore, the calibration paper is used to observe the distorted image through a transparent structure; and the calibration paper is used to observe the image before distortion, which is basically corrected, through the outer casing of the structure.

[0009] Furthermore, if it is inconvenient to cover the transparent structure under test with an outer casing, a proportionally scaled model of the transparent material can be constructed, which can be used only to obtain the mapping relationship before and after distortion.

[0010] A method for correcting image distortion of the flow field inside a transparent structure based on affine and B-spline mesh transformation is described below:

[0011] Step 1: Read in the calibration paper images before and after distortion I fixed and I float Construct a function to map the distorted image to the undistorted image. The mapping function is T(x, y), where x and y are the two directions of the two-dimensional transformation. The transformation method includes the overall transformation T. global (x, y) and local transformation T local (x, y), that is:

[0012] T(x, y) = T global (x, y) + T local (x, y);

[0013] Step 2: Perform a global transformation on the image using affine transformation. Affine transformations in 2D images have four transformations (translation, rotation, scaling, and shear) and seven degrees of freedom, represented as:

[0014]

[0015] θ 11 θ 12 θ 13 θ21 θ 22 θ 23 These are the transformation parameters for the affine transformation.

[0016] Step 3: Perform local transformation on the image using B-spline mesh transformation. This involves constructing a uniformly distributed B-spline control point mesh with a spacing of δ, and the displacement value of each control point (mesh node) is Φ. j，j The displacement value of each pixel in the image is fitted by the transformation of control points. Influenced by the displacement values ​​of its surrounding 4×4 control points, the local transformation of the distorted image can be achieved by controlling the displacement of the grid nodes. When a control point is displaced, it only causes a local transformation in pixels within a limited surrounding area.

[0017]

[0018] in, B0(t)~B3(t) are cubic B-spline basis functions, x and y are the coordinates of arbitrary points, δ is the grid node spacing, t is a variable, and Φ is the node displacement value.

[0019]

[0020]

[0021]

[0022]

[0023] To ensure that the free deformation based on splines is smooth, a penalty term λC is introduced. smooth Using (T) for regularization, the cost function of the orthodontic model is:

[0024] C(θ, Φ) = -C similarity (T(I float ), I fixed )+λC smooth (T)

[0025]

[0026]

[0027] Among them, H(T(I) float )), H(I fixed) H(T(I)) represents the boundary entropy of the two images, respectively. float ), I fixed) The joint entropy representing them is calculated from the joint histogram of the two images, where λ is the regularization coefficient, X and Y are the maximum coordinates of the image in the x and y directions, respectively, and N is the number of pixels in the image.

[0028] Step 4: The pixel coordinates of the transformed image correspond to the integer coordinates of the fixed image. Therefore, the coordinates before the transformation will have non-integer values. So, bicubic interpolation is needed for these non-integer coordinates.

[0029] Step 5: Find the optimal transformation that minimizes the cost function of the orthodontic model, and use the LBFGS method as the optimization algorithm;

[0030] Step 6: Apply the optimal transformation inversely to the flow image inside the structure under direct shooting conditions to obtain the true flow situation without distortion.

[0031] The beneficial effects of this invention are as follows:

[0032] The orthodontic effect of the correction system was verified through flow field experiments inside the pipe. The application of PIV technology to flow field research within transparent structures not only improves measurement accuracy but also provides a more precise characterization of flow field features. Furthermore, the 2D3C PIV system better showcases the three-dimensional flow characteristics within the flow field. While achieving refractive index matching between the solid and liquid phases through solution mixing is not suitable for large-scale aquatic environments, this invention addresses the flow field or field of view itself. Based on geometric optics, it utilizes post-processing techniques and image orthodontics to process PIV measurement results and perform computational analysis. The post-processing algorithm uses a non-rigid registration model based on normalized mutual information to describe the flow field motion within the transparent structure, and the image orthodontics method based on affine and B-spline mesh transformation provides high flexibility for the flow field motion. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the overall structure of the present invention;

[0034] Figure 2 This is the overall flowchart of the present invention;

[0035] Figure 3 This is an image of the calibration paper before distortion in the test of this invention;

[0036] Figure 4 This is an image of the calibration paper after distortion in the test of this invention;

[0037] Figure 5 Using the present invention to Figure 3 and Figure 4 The image of the calibration paper after orthodontic transformation;

[0038] Figure 6 This is an average velocity field diagram at a certain moment before the distortion of the PIV test in this invention;

[0039] Figure 7This is an average velocity field diagram at a certain moment after the PIV test distortion of this invention;

[0040] Figure 8 This is the average velocity field diagram at a certain moment after the PIV test orthodontic treatment of this invention. Detailed Implementation

[0041] The present invention will now be further described with reference to the accompanying drawings.

[0042] like Figure 1 The diagram shown is a schematic representation of the overall structure of the present invention, including: a transparent structure 1, a structural outer casing 2, a propeller 3, a motor 4, an aluminum profile frame 5, a first high-speed camera 6-1, a second high-speed camera 6-2, a synchronizer 7, a laser 8, and a computer 9.

[0043] This invention designs an optical measurement system and method for the internal flow field of a transparent structure based on affine and B-spline mesh transformation for use in fluid mechanics experimental water tanks. The system includes calibration paper, an outer casing for the structure, a PIV system, and a post-processing algorithm. The calibration paper is as follows... Figure 2 As shown, calibration paper is embedded in a transparent structure 1 and covers the test plane, allowing direct observation of the distorted image. The structure is then encased in a watertight chamber 2 filled with the solution within the structure. The observation window, visible from the outside of the chamber, is planar, indicating that the image distortion has been largely corrected. The PIV system consists of two high-speed cameras 6-1 and 6-2, a laser 8, a synchronizer 7, and a computer 9. Post-processing software obtains the polynomial mapping relationship between image points before and after distortion. This mapping relationship is then applied inversely to the flow image inside the structure under direct shooting conditions, allowing for the acquisition of the undistorted, true flow. The corrective effect is verified using PIV test data of the flow field within the pipe.

[0044] The workflow of the optical measurement method for the internal flow field of transparent structures based on affine and B-spline mesh transformation is as follows: The first step is the preparation of the experiment and the calibration of images before and after distortion. Setting up the PIV experimental platform mainly includes the installation of the experimental model and the placement of the high-speed camera and laser. Model installation requires leveling and aligning a small desktop optical experimental platform. The high-speed camera is placed on a horizontal base and observed from the left and right front of the area to be measured at a certain tilt angle. First, the camera is calibrated, and then images before and after distortion are captured on the built-in calibration paper, such as... Figure 3 As shown in Figure 4, the specific method involves placing the standard calibration paper on the camera's shooting plane. The image captured directly through the transparent structure 1 is the distorted image of the experimental group. Figure 4 The image observed after the outer casing 2 of the structure was watertight is a control group image before distortion, as shown in the figure. Figure 3The first step involves aligning the calibration paper plane with the laser plane and capturing a clear image of the calibration paper pattern using a high-speed camera. The second step involves scattering polyamide particles with an average diameter of 50 μm within a transparent structure as tracer particles. PIV (Pipeline Induction) tests are then conducted on the pipe flow field under experimental platform conditions. Tests are performed on an experimental group with some distortion under normal conditions and a control group with matched refractive indices at three different propeller speeds. Once the flow field stabilizes, the particle images flowing within the pipe are directly recorded using a CCD high-speed camera. The third step involves post-processing using an image orthogonal algorithm. Orthogonal methods based on affine and B-splines are used to process the calibration plate images before and after distortion, establishing a polynomial mapping relationship between feature points before and after distortion. Transformation equations are then used to orthogonally restore the distorted particle images. Specifically, the distortion correction coefficients are calculated based on the actual positions of the effective grid nodes corresponding to the target flow field. Finally, these correction coefficients are imported into the original PIV measurement data of the pipe flow field after image binarization, and the original vector field is corrected to obtain the corrected PIV measurement results of the pipe flow field. The orthogonal method flow is as follows: Figure 2 As shown. The fourth step is image preprocessing, which involves extracting the velocity field from the particle displacement map of the digitized two-dimensional fluid image. After correcting the particle image using the aforementioned optical distortion correction method, the velocity distribution of the flow field in the pipe before and after correction is calculated using an adaptive cross-correlation algorithm. Specifically, the image is processed using Dynamic Studio 7.5 software to remove the background, perform adaptive cross-correlation analysis, conduct 2D3C analysis based on the calibration file, calculate the time-averaged velocity field, and smooth it using filtering. The fifth step is to compare the correction results with the control group experimental results to verify the feasibility of the distortion method. The average velocity field when the propeller rotates to the same position per revolution is selected for comparison. Figure 6 , 7 As shown in Figure 8.

[0045] In summary, this invention provides a method and experimental apparatus for correcting image distortion generated during flow field testing within transparent structures. It obtains particle image sequences before and after distortion, establishes a mapping relationship between feature point polynomials before and after distortion, and uses transformation equations to orthogonally restore the distorted particle images. The correction results are compared with control group experimental results to verify the feasibility of the distortion correction method, and the measurement results are analyzed.

[0046] To address the flow field distortion problem caused by the difference in refractive index between solid and liquid phases, a nonlinear image correction method based on affine and B-spline mesh transformation is proposed. By obtaining the coordinate mapping relationship of particle image sequences before and after distortion, the image distortion problem caused by the difference in refractive index is solved from the data level.

[0047] If it is inconvenient to cover the structure under test with the outer casing 2, a scale model with the same transparent material can be constructed and used only for the step of obtaining the mapping relationship before and after distortion.

[0048] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A system for correcting image distortion of the flow field inside a transparent structure based on affine and B-spline mesh transformation, characterized in that: A transparent structure to be tested (1) has a flow field to be tested inside it; a casing (2) for the structure is a watertight casing with an optical plane, the casing (2) covers the transparent structure to be tested (1), and the casing is filled with a solution that matches the refractive index of the transparent structure to be tested (1); calibration paper is built into the transparent structure to be tested (1) and covers the plane to be tested; a PIV system, including optical measurement equipment, is used to acquire: the distorted image (I) obtained by directly observing the calibration paper inside the transparent structure to be tested (1). float ); The image before distortion (I) obtained by observing the calibration paper inside the transparent structure under test (1) through the outer casing of the structure. fixed The PIV system includes a first high-speed camera (6-1), a second high-speed camera (6-2), a synchronizer (7), a laser (8), and a computer (9). The first high-speed camera (6-1), the second high-speed camera (6-2), the laser (8), and the computer (9) are all connected to the synchronizer (7). The post-processing algorithm calculates the distorted image (I) through affine transformation and B-spline mesh transformation. float ) to pre-distortion image (I fixed The nonlinear distortion mapping relationship is obtained, and this mapping relationship is applied inversely to the correction of the real flow field image.

2. The image distortion correction system for the flow field inside a transparent structure based on affine and B-spline mesh transformation according to claim 1, characterized in that: If it is inconvenient to cover the transparent structure (1) with the outer box (2), a transparent material model of the same scale can be constructed and used only for obtaining the mapping relationship before and after distortion.

3. A method for correcting image distortion of the flow field inside a transparent structure based on affine and B-spline mesh transformation, characterized in that: The specific steps are as follows: Step 1: Read in the calibration paper images before and after distortion I fixed and I float Construct a function to map the distorted image to the undistorted image. The mapping function is T(x,y), where x and y are the two directions of the two-dimensional transformation. The transformation method includes the overall transformation T. global (x,y) and local transformation T local (x,y), that is: T(x,y)=T global (x,y)+T local (x,y); Step 2: Perform a global transformation on the image using affine transformation. Affine transformations in 2D images have four transformations (translation, rotation, scaling, and shear) and seven degrees of freedom, represented as: θ 11 θ 12 θ 13 θ 21 θ 22 θ 23 The transformation parameters are those for the affine transformation. Step 3: Perform local transformation on the image using B-spline mesh transformation. This involves constructing a uniformly distributed B-spline control point mesh with a spacing of δ, and the displacement value of each control point (mesh node) is Φ. i,j The displacement value of each pixel in the image is fitted by the transformation of control points. Influenced by the displacement values ​​of its surrounding 4×4 control points, the local transformation of the distorted image can be achieved by controlling the displacement of the grid nodes. When a control point is displaced, it only causes a local transformation in pixels within a limited surrounding area. in, B0(t)~B3(t) are cubic B-spline basis functions, x,y are the coordinates of arbitrary points, δ is the grid node spacing, t is a variable, and Φ is the node displacement value; To ensure that the free deformation based on splines is smooth, a penalty term λC is introduced. smooth Using (T) for regularization, the cost function of the orthodontic model is: C(θ,Φ)=-C similarity (T(I float ),I fixed )+λC smooth (T) Among them, H(T(I) float )), H(I fixed H(T(I)) represents the boundary entropy of the two images, respectively. float ),I fixed ) represents their joint entropy, calculated from the joint histogram of the two images, λ is the regularization coefficient, X and Y are the maximum coordinates of the image in the x and y directions, respectively, and N is the number of pixels in the image; Step 4: The pixel coordinates of the transformed image correspond to the integer coordinates of the fixed image. Therefore, the coordinates before the transformation will have non-integer values. So, bicubic interpolation is needed for these non-integer coordinates. Step 5: Find the optimal transformation that minimizes the cost function of the orthodontic model, and use the LBFGS method as the optimization algorithm; Step 6: Apply the optimal transformation inversely to the flow image inside the structure under direct shooting conditions to obtain the true flow situation without distortion.

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