Method for obtaining temperature of discharge channel from schlieren image based on abel inversion

Abstract

The application discloses a kind of based on abel inverse transform from schlieren image obtains discharge channel temperature method, belong to image processing technical field, the method includes: to each row in gray scale measurement value variation matrix is obtained temperature measurement value matrix by abel inverse transform, consider the influence law of gray scale value error and temperature value error in abel transformation process;The center point position of each row of temperature measurement value matrix is used to determine the center axis of temperature measurement value matrix, and the accuracy of the algorithm is improved by accurately searching the center axis of discharge channel;The maximum and minimum of each column of temperature measurement value variation matrix are used to determine the corresponding target value range, and the column vectors in the preset temperature value variation matrix of the same size as the temperature measurement value variation matrix are sequentially determined, the true temperature value is efficiently and accurately separated from the measurement value, the accuracy of the schlieren system for measuring the temperature of discharge channel is improved, and has strong anti-noise ability.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of image processing, and more particularly relates to a method for obtaining discharge channel temperature from schlieren image based on Abel inverse transform. BACKGROUND

[0002] The calibrated quantitative schlieren system is an effective means for measuring the temperature of long gap discharge channel and plays an important role in the study of discharge channel thermal characteristics. The schlieren picture measured by the schlieren system needs to be inverted to the corresponding temperature value through Abel inverse transform. Abel inverse transform is an algorithm for reconstructing axisymmetric or spherically symmetric three-dimensional objects from two-dimensional projection information, and is commonly used in the reconstruction of axisymmetric, optically thin flames, plumes or plasmas. It has been widely used in many fields such as mechanics, spectroscopy, seismology, plasma physics and scattering theory. The research on the solution method of Abel inverse transform has been in-depth, and the algorithm has been continuously improved. However, Abel inverse transform is a typical ill-posed problem, and as a kind of ill-conditioned equation, a small disturbance in the input quantity will have a great influence on the output result. In practical applications, for example, due to the problems of shooting means and shooting instruments, noise is inevitably mixed in the schlieren picture, resulting in a large error in the calculation result of Abel inverse transform; in addition, the limitation of the time and space resolution of the schlieren picture makes it difficult to determine the noise component and the center point is not accurate, which further increases the error in the calculation result. Due to the uncertainty of noise and the resolution limitation of the schlieren picture, it is difficult to completely filter out the noise by conventional algorithms, and the error caused by small noise will have a great influence on the calculation result. Designing high-precision Abel inverse transform algorithm under noise interference can more accurately realize the inversion of discharge channel temperature, and has important reference and reference significance for the reconstruction and characteristic research of three-dimensional objects in other application fields.

[0003] At present, noise in the schlieren picture is inevitable during shooting and difficult to filter out by existing means; there are many algorithms with noise resistance ability for Abel inverse transform, such as Fourier-Hankel transform method, discrete regularization method, etc., but their noise resistance ability is limited, and the calculation result still has a large error in the application of schlieren system. Especially in the calculation of the temperature of the leader channel with high center temperature, the calculation result deviates seriously from the true temperature. SUMMARY

[0004] In view of the above defects or improvement needs of the prior art, the present application provides a method for obtaining discharge channel temperature from schlieren image based on Abel inverse transform, which aims to solve the technical problem that the temperature result corresponding to the discharge channel schlieren image has a large error.

[0005] To achieve the above object, according to one aspect of the present application, a method for obtaining temperature of discharge channel from striae image based on Abelian inverse transformation is provided, comprising:

[0006] S1: constructing a gray scale measurement value variation matrix corresponding to a gray scale measurement value matrix of striae image of discharge channel; and performing Abelian inverse transformation on each row in the gray scale measurement value variation matrix to obtain a temperature measurement value matrix;

[0007] S2: determining a central axis of the temperature measurement value matrix by using a central point position of each row of the temperature measurement value matrix; aligning positions of the temperature measurement value matrix and the gray scale measurement value variation matrix by using the central axis; obtaining a temperature measurement value variation matrix corresponding to a part of the temperature measurement value matrix on one side of the central axis, and maximum value and minimum value of each column of the temperature measurement value variation matrix;

[0008] S3: determining a target value range corresponding to each column of the temperature measurement value variation matrix by using the maximum value and the minimum value, and sequentially determining each column vector in a preset temperature value variation matrix of the same size as the temperature measurement value variation matrix, wherein element values in each column vector are within the corresponding target value range;

[0009] S4: performing mirror image of a preset temperature value matrix corresponding to the preset temperature value variation matrix with the central axis and splicing to obtain a temperature real value matrix.

[0010] In one embodiment, the S1 of constructing a gray scale measurement value variation matrix corresponding to a gray scale measurement value matrix of striae image of discharge channel comprises:

[0011] selecting a section from the striae image of discharge channel as a target striae image; the selection principle is that a section of striae image of discharge channel with vertical downward and without branch is selected as the target striae image, and the length of the target striae image in the vertical direction is as long as possible and the number of gray scale value rows is as many as possible, and the horizontal range is selected to completely cover the discharge channel while the number of gray scale value columns is as few as possible;

[0012] obtaining a gray scale measurement value matrix of the target striae image;

[0013] subtracting adjacent columns of the gray scale measurement value matrix to obtain element values of corresponding columns in the gray scale measurement value variation matrix.

[0014] In one embodiment, the obtaining a gray scale measurement value matrix of the target striae image comprises:

[0015] The columns in the original gray value matrix of the target schlieren image are meaned, and the number of columns closest to the center axis is denoted as o; the number of columns of the minimum value of the gray value in each row and the number of columns of the maximum value of the gray value are found; each row is intercepted with o as the center point and K*(b-a) as the radius to obtain the gray measurement value matrix of the target schlieren image; K is a preset multiple to obtain the gray value matrix covering the discharge channel.

[0016] In one of the embodiments, the S3 comprises:

[0017] S31: determining the target value range corresponding to each element in the preset temperature value change matrix by using the maximum value and the minimum value of each column of the temperature measurement value change matrix; determining X i in each element in the corresponding target value range;

[0018] S32: detecting whether the temperature in the determined X i corresponding temperature true value matrix meets the physical constraint; if not, fine-tuning it until it meets the physical constraint; taking the corresponding temperature value meeting the physical constraint as the true X i , defining X k-1 , obtaining each column vector in the preset temperature value change matrix X=[X1,X2,…,X k-1 of the same size as the temperature measurement value change matrix.

[0019] In one of the embodiments, the S31 comprises:

[0020] Assigning the two boundary endpoints of the interval [x1x2] to the jth column element x i in X ij corresponding to the product of the objective function value; if the product is greater than 0, the interval [x1x2] is expanded; wherein the objective function is: L1=g1 i(j+1) -g0 i(j+1) , g1 i(j+1) is the gray measurement value change, g0 i(j+1) is the preset gray value change; x1 and x2 are the minimum value and the maximum value of the jth column of the temperature measurement value change matrix;

[0021] Assigning the interval boundary endpoints after the interval expansion to x ij corresponding to the product of the objective function value; if the product is greater than 0, the current interval will continue to be expanded, until the product of the objective function value corresponding to the boundary endpoints of the current interval (x1′+x2′) is less than 0, and the current interval (x1′+x2′) is taken as the maximum value range corresponding to x ij ;

[0022] Let x0=(x1′+x2′) / 2, and denote x ijL10, x i L11; if L11*L10<0, then let x2'=x0, otherwise let x1'=x0, to obtain a new interval (x1"+x2"), and continue to take the interval midpoint to gradually reduce x ij , until the current interval (x1""+x2"") boundary endpoints are assigned x ij , the corresponding target function value product is lower than the first minimum threshold value; the current interval (x1""+x2"") is taken as x ij , the corresponding target value range is determined, and x ij is obtained in the corresponding target value range, and a column vector X i is further obtained.

[0023] In one of the embodiments, the S31 comprises:

[0024] Let X i be a column vector, and the jth column element x ij is located in the interval 2*[x1x2], let x0=(x1+x2) / 2, Δx=(x2-x1) / 2; x1 and x2 are the minimum value and the maximum value of the jth column of the temperature measurement change amount matrix;

[0025] A preset vector [x0-2Δx, x0-Δx, x0, x0+Δx, x0+2Δx] is constructed; x ij , respectively, are equal to the corresponding target function values L2=|g1 i(j+1) -g0 i(j+1) | 2 +|g1 i(2k-1-j )+g0 i(j+1) | 2 , g1 i(j+1) , g1 i(2k-1-j) are the gray scale measurement change amounts, and g0 i(j+1) is a preset gray scale change amount;

[0026] The value corresponding to the minimum target function value is recorded as x0, and then Δx is changed to half of the original Δx / 2, the preset vector corresponding to Δx / 2 is constructed, and x ij , respectively, are equal to the corresponding target function values, the value corresponding to the minimum target function value is recorded as the new x0, and the process is continued until x ij , respectively, are equal to the corresponding target function values, and the value corresponding to the minimum target function value is recorded as the new x0, and the process is continued until x ij = x0, and a column vector X i is further obtained.

[0027] In one of the embodiments, the physical constraint is that the temperature corresponding to any element in the temperature real value matrix corresponding to the preset temperature value variation matrix X has a radial temperature difference greater than an axial temperature difference.

[0028] According to another aspect of the present application, there is provided a device for obtaining temperature of a discharge channel from a striae image based on Abelian inverse transformation, comprising:

[0029] A constructing module is configured to construct a gray scale measurement value variation matrix corresponding to a gray scale measurement value matrix of the striae image of the discharge channel, and perform Abelian inverse transformation on each row in the gray scale measurement value variation matrix to obtain a temperature measurement value matrix;

[0030] An aligning module is configured to determine a central axis of the temperature measurement value matrix by using central point positions of each row of the temperature measurement value matrix, to positionally align the temperature measurement value matrix with the gray scale measurement value variation matrix by using the central axis, to obtain a temperature measurement value variation matrix corresponding to a portion of the temperature measurement value matrix on one side of the central axis, and to obtain maximum values and minimum values of each column of the temperature measurement value variation matrix;

[0031] A determining module is configured to determine a respective target value range by using the maximum values and the minimum values of each column of the temperature measurement value variation matrix, and to sequentially determine each column vector in a preset temperature value variation matrix of the same size as the temperature measurement value variation matrix, with element values in each column vector being within the corresponding target value range.

[0032] A transforming module is configured to mirror and splice a preset temperature value matrix corresponding to the preset temperature value variation matrix X with the central axis to obtain a temperature real value matrix.

[0033] According to another aspect of the present application, there is provided an image processing device comprising a memory and a processor, the memory storing a computer program, and the processor implementing the steps of the above method when executing the computer program.

[0034] According to another aspect of the present application, there is provided a computer readable storage medium storing a computer program, the computer program being executed by a processor to implement the steps of the above method.

[0035] Overall, the above technical solutions conceived by the present application can achieve the following beneficial effects compared with the prior art:

[0036] (1) The application provides a method for obtaining discharge channel temperature from a schlieren image based on an Abel inverse transform, an Abel inverse transform is performed on each row in the gray value measurement change matrix to obtain a temperature measurement value matrix, a directional method for constructing and adjusting the temperature value matrix is proposed according to the influence law of gray value error and temperature value error in the Abel transform process, the center axis of the temperature measurement value matrix is determined by using the center point position of each row of the temperature measurement value matrix, the discharge channel center axis can be accurately searched, and the accuracy of the algorithm is improved, the maximum value and the minimum value of each column of the temperature measurement value change matrix are used to determine the corresponding target value range, and each column vector in the preset temperature value change matrix with the same size as the temperature measurement value change matrix is sequentially determined, so that the temperature true value is efficiently and accurately separated from the measurement value, the accuracy of the schlieren system in measuring the discharge channel temperature is improved, and the anti-noise capability is strong.

[0037] (2) In the scheme, a selection principle for selecting a section from the discharge channel schlieren image as a target schlieren is provided: a section of the discharge channel schlieren image with a vertical downward direction and without branches is taken as the target schlieren image, the longitudinal selection of the target schlieren image is as long as possible, the number of gray value rows is as large as possible, and the transverse selection range fully covers the discharge channel while the number of gray value columns is as small as possible; in this way, the method for obtaining the discharge channel temperature from the schlieren image based on the Abel inverse transform can be realized with the lowest calculation complexity while ensuring the accuracy of temperature calculation, and further, the execution efficiency of the entire algorithm can be improved.

[0038] (3) In the scheme, a method for obtaining the gray value measurement matrix of the target schlieren image is provided, each row is taken as a center point with o, and a radius of K*(b-a) is taken to obtain the gray value measurement matrix of the target schlieren image; this method is also used to reduce the calculation complexity while ensuring the maximum details of the discharge channel schlieren image to the greatest extent, so as to ensure the accuracy of the finally determined temperature.

[0039] (4) In the scheme, the determined X i corresponding to the temperature true value matrix is detected to see whether the temperature meets the physical constraint; if not, the temperature is fine-tuned until the temperature meets the physical constraint; the Abel inverse transform data features and the discharge channel temperature characteristics are summarized from the information space and the physical space respectively, the true value in the Abel inverse transform is separated from the measurement value by using the information-physical fusion idea, and the accuracy is high.

[0040] (5) The scheme provides a method for determining each vector in the preset temperature value change matrix by using the dichotomy method, the maximum value and the minimum value corresponding to each row are used to find out X ieach element in X is gradually reduced by using bisection method, until the minimum value range is found as the target value range, and X is determined in the target value range i each element in X is gradually reduced by using bisection method, until the minimum value range is found as the target value range, and X is determined in the target value range i The method uses bisection method, and the determined X i is accurate.

[0041] (6) The method for determining each vector in the preset temperature value change matrix by using interval approximation method is provided, the preset vector corresponding to the boundary is constructed, the target function value corresponding to each element in X i is obtained, the boundary is gradually reduced according to the value corresponding to the minimum target function value, and the minimum boundary is found, and X i corresponding element value is determined in the target value range; the method has low calculation complexity, can quickly find the closest interval, and then determine the corresponding element value in X i .

[0042] (7) The physical constraint is provided, and the radial temperature difference of the temperature corresponding to any element in the temperature true value matrix is greater than the axial temperature difference, so that the noise characteristics on the temperature can be eliminated with low calculation complexity. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 The overall flowchart of the method for acquiring the discharge channel temperature from the schlieren image based on the Abel inverse transformation provided in Embodiment 1 of the present application is shown;

[0044] Figure 2 The transformation relationship diagram of each physical quantity in the Abel inverse transformation process provided in Embodiment 1 of the present application is shown;

[0045] Figure 3 The algorithm flowchart of the automatic search for the optimal center point in the Abel inverse transformation process provided in Embodiment 1 of the present application is shown;

[0046] Figure 4 The specific flowchart of the specific algorithm of the method for acquiring the discharge channel temperature from the schlieren image based on the Abel inverse transformation provided in Embodiment 1 of the present application is shown;

[0047] Figure 5a The schematic diagram of the temperature value change on the left side of the center point of the temperature measurement value matrix provided in Embodiment 1 of the present application is shown;

[0048] Figure 5b The schematic diagram of the temperature value on the left side of the center point of the temperature measurement value matrix provided in Embodiment 1 of the present application is shown;

[0049] Figure 5c A comparison chart of the entire cross-section gray value variation amount and the original gray value variation amount obtained from the temperature value provided for the embodiment 1 of the present application;

[0050] Figure 6a A striae image provided for the embodiment 1 of the present application;

[0051] Figure 6b A schematic chart of the temperature value true value obtained by the algorithm provided for the embodiment 1 of the present application;

[0052] Figure 6c A schematic chart of the gray value variation amount true value obtained by the algorithm provided for the embodiment 1 of the present application;

[0053] Figure 6d A schematic chart of the gray value variation amount error obtained by the algorithm provided for the embodiment 1 of the present application;

[0054] Figure 6e A comparison chart of the cross-section temperature value and the temperature true value obtained by the algorithm provided for the embodiment 1 of the present application;

[0055] Figure 6f A schematic chart of the absolute error of the temperature value obtained by the algorithm provided for the embodiment 1 of the present application;

[0056] Figure 6g A schematic chart of the relative error of the temperature value obtained by the algorithm provided for the embodiment 1 of the present application. DETAILED DESCRIPTION

[0057] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and should not be used to limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0058] Embodiment 1

[0059] As Figure 1As shown, this embodiment provides a method for obtaining the discharge channel temperature from the schlieren image based on the inverse Abel transform, including: S1-S4. S1: Constructing a grayscale measurement value variation matrix corresponding to the grayscale measurement value matrix of the schlieren image of the discharge channel; performing an inverse Abel transform on each row in the grayscale measurement value variation matrix to obtain a temperature measurement value matrix. S2: Determine the central axis of the temperature measurement value matrix using the center point position of each row of the temperature measurement value matrix; align the temperature measurement value matrix with the grayscale measurement value variation matrix using the central axis; obtain the temperature measurement value variation matrix corresponding to the portion of the aligned temperature measurement value matrix on one side of the central axis, as well as the maximum and minimum values ​​of each column of the temperature measurement value variation matrix. S3: Determine the corresponding target value range using the maximum and minimum values ​​of each column of the temperature measurement value variation matrix, and determine the preset temperature value variation matrix X=[X1, X2,…, X] of the same scale as the temperature measurement value variation matrix in turn. k-1 ], the element values ​​in each column vector are within the corresponding target value range. S4: The preset temperature value matrix corresponding to the preset temperature value change matrix X is mirrored about the central axis and spliced ​​to obtain the temperature true value matrix.

[0060] It should be understood that although Figure 1 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. In addition, Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0061] Specifically, S1, a certain range of grayscale values ​​are selected from the schlieren image of the discharge channel to form a grayscale value matrix; each row is interpolated 5 times and the background schlieren is subtracted to obtain a grayscale measurement value change matrix; each row of the grayscale measurement value change matrix is ​​subjected to an inverse Abel transform to obtain a temperature measurement value matrix and the center point position of each row.

[0062] After interpolation, the gray value matrix is ​​subjected to inverse Abel transformation, and the transformation relationship of each physical quantity is as follows: Figure 2Wherein, when multiple rows of gray scale values are subjected to Abel inverse transform, in order to fully utilize data and find a center point, an algorithm can be designed to automatically search for an optimal center point. The principle for determining the center point is that when Abel inverse transform integration is performed on the left and right sides of the center point for a row of gray scale values, the integration results at the center point are the same. The specific method for searching for the center point is as follows: first, a hypothetical zero point is found, and then the left 5 points are taken as center points in turn from left to right. When traversing, Abel inverse transform integration is performed on the left and right sides of a certain point taken as a center point, and the difference between the integration results of the center points on the left and right sides is denoted as cri. When the signs of cri at two consecutive sampling points are opposite, it can be determined that the center point is located between the two sampling points. The center point is determined by using the dichotomy method between the two points until cri is small enough or the number of samplings is large enough. The specific process is as follows: Figure 3 .

[0063] Regarding the analysis of the Abel inverse transform process, it needs to be explained that the Abel inverse transform process and error distribution characteristics are as follows: the process from gray scale values to density values is the Abel inverse transform process; the process from the true value of the density value to the true value of the gray scale value through the Abel forward transform process can be obtained, and the calculation error in this process is very small and can be ignored. After the Abel transform, the temperature value and the density value are one-to-one corresponding, and the temperature value distribution is approximately Gaussian distribution according to experience. The true value and the noise value in the Abel transform process are independent of each other. The error distribution of the gray scale value is uniform, and the density function is approximately Gaussian distribution; the error of the density value presents a distribution of large in the middle and small on both sides; the error of the temperature value presents a distribution of very large in the middle and small on both sides. Although the temperature calculation result has an error, the channel center position and the radius size reflected thereby have certain reference value. The relative density error at the radius r is:

[0064]

[0065] Regarding the analysis of the Abel forward transform process, the error of the gray scale value variation at the coordinate y is:

[0066]

[0067] Wherein, Δδρ(r) is the relative density error at the radius r, n0 is the air refractive index, Δg(y) is the error of the gray scale value variation at the coordinate y, k is the slope of the calibration curve, and f is the focal length of the lens.

[0068] The error rule of Abel inverse transform is: according to the Abel inverse transform error derivation formula, the density error of any point is accumulated by the gray value error of the corresponding coordinates outside the point, that is, the gray value error of any point may cause the density value error of the internal part of the point, and the closer to the point, the greater the error, and the farther away from the point, the smaller the error; if the gray value error of a point and a plurality of continuous points outside is 0, the density value error of the corresponding coordinates is 0. According to the Abel inverse transform error derivation formula, the gray value error of any point is accumulated by the density error outside the point; if the density error outside a certain point is known to be 0, the gray value error of the point is caused by the density error of the corresponding coordinates of the point. According to this idea, if the gray value obtained from the density value coincides with the true gray value, the density error value is considered to be 0, and the density value is the true value. The density value corresponds to the temperature value one by one, so for the temperature value vector, the temperature value change can be adjusted from the outside to the inside point by point according to the gray value, so that the error is 0.

[0069] Specifically, S2, the center axis position in the temperature measurement value matrix is determined; the temperature measurement value matrix and the gray measurement value change matrix position are aligned by using the center axis position; the left part of the aligned temperature measurement value matrix center axis is taken, and the temperature measurement value change matrix is obtained by column difference, and then the maximum value and the minimum value of each column are taken to form the temperature measurement value change maximum value and minimum value vector.

[0070] For example, the gray measurement value change matrix is as follows: The corresponding temperature measurement value matrix is as follows: Wherein, the gray value change of each row is roughly centered on the center point, and is centrally symmetrically distributed; each row of temperature is centered on the center point and symmetrically distributed on the left and right sides.

[0071] The center axis position is the average value of the column where the center point is located, and is taken as k1, and is taken as k; the temperature measurement value matrix is aligned, and the steps are as follows: the temperature values of each row are centered on the center point, and k-1 points are taken on the left and right sides, and the center points of the temperature values of each row are aligned, that is, the center axis, and the aligned temperature measurement value matrix T1 is as follows:

[0072]

[0073] Further, the gray measurement value change matrix position is aligned, and the steps are as follows: the gray value change of each row is centered on the center axis position k1, and k-1 points are sampled on the left and right sides with the same resolution as the resolution of the gray measurement value change matrix, and the aligned gray measurement value change matrix G1 is as follows:

[0074]

[0075] The temperature measurement value change amount matrix, the acquisition formula is:

[0076]

[0077] The temperature measurement value change amount maximum value and minimum value vector is a vector dT composed of the maximum value and the minimum value of each column of the matrix dT max , dT min .

[0078] The preset temperature value change amount matrix is as follows:

[0079]

[0080] The preset temperature value matrix is as follows:

[0081]

[0082] Wherein, t0 i1 = 300, 1≤i≤m; 1≤i≤m, j>1.

[0083] The preset gray value change amount matrix is as follows:

[0084]

[0085] Wherein, G0 i is obtained by Abel positive transformation of [t0 i1 , t0 i2 , …, t0 ik ]; the preset temperature value matrix is in the transformation adjustment process, the corresponding preset temperature value matrix and the preset gray value change amount matrix are also changing.

[0086] Specifically, S3, all elements in the preset temperature value change amount matrix of the same size as the temperature measurement value change amount matrix are zero X=[X1, X2, …, X k-1 ]=0, X is accumulated from the left side from 300 column by column to obtain the preset temperature value matrix T0=[T01, T02, …, T0 k ], each row of the preset temperature value matrix is subjected to Abel positive transformation to obtain the preset gray value change amount matrix G0. Determine X1 by using bisection method or interval approximation method; then determine X2 in the same way, and so on, until X k-2 is determined. Finally, define the last vector, such as X k-1 =X k-2 / 4, the entire preset temperature value change amount matrix X is determined.

[0087] Specifically, the preset temperature value matrix T0 corresponding to the preset temperature value change matrix X is axisymmetric with the center axis as the center to obtain a complete temperature real value matrix, and the preset gray value change matrix G0 is center-symmetric with the center axis as the center to obtain a complete real gray value change matrix. The process of determining the gray value from one row of temperature value changes is as follows Figure 5a 、 Figure 5b and Figure 5c .

[0088] It should be noted that the actual parameters such as the number of times, the number of rows, the left side, the right side, etc. are used for illustration, and the actual values can be set as needed according to the actual scene.

[0089] As an optional implementation, the gray scale measurement value change matrix corresponding to the gray scale measurement value matrix of the discharge channel schlieren image in S1 includes: selecting a section as a target schlieren image from the discharge channel schlieren image; the selection principle is: selecting a section of the discharge channel schlieren image with a vertical downward direction and without branches as the target schlieren image, and the longitudinal direction of the target schlieren image is as long as possible and the number of gray scale values is as much as possible, and the horizontal direction of the target schlieren image should not be too wide, so that the number of gray scale values is as small as possible, and the principle is to completely cover the discharge channel. The horizontal direction should not be too wide, so that the number of gray scale values is as small as possible while completely covering the discharge channel. Obtain the gray scale measurement value matrix of the target schlieren image; subtract the adjacent columns of the gray scale measurement value matrix to obtain the elements of the corresponding columns in the corresponding gray scale measurement value change matrix.

[0090] As an optional implementation, the gray scale measurement value matrix of the target schlieren image includes: performing mean value processing on each column in the original gray scale value matrix of the target schlieren image, and taking the number of columns closest to the center axis as o; finding the column number a of the minimum gray scale value and the column number b of the maximum gray scale value in each row; each row is centered on o and has a radius of K*(b-a) to obtain the gray scale measurement value matrix of the target schlieren image; K is a preset multiple to obtain a gray scale value matrix covering the discharge channel, and K can be set to 1.1-1.3.

[0091] As an optional implementation, S3 includes: S31: determining the target value range corresponding to each element in X using the maximum value and the minimum value of each column of the temperature measurement value change matrix; determining each element in X within the corresponding target value range; S32: detecting whether the temperature in the temperature real value matrix corresponding to the determined X meets the physical constraint; if not, fine-tuning it until it meets the physical constraint; taking the corresponding temperature value that meets the physical constraint as the real X i , the user-defined X k-1 , to obtain a preset temperature value change matrix X of the same size as the temperature measurement value change matrix X=[X1, X2,..., X k-1] in each column vector. The specific process is as follows Figure 4 .

[0092] As an optional implementation, S31 includes: obtaining two boundary endpoints of the interval [x1x2] and assigning them to X i The j-th column element x in ij The product of the corresponding objective function values ​​when L1 is equal to 1; if the product is greater than 0, the interval [x1x2] will be expanded; where the objective function is: L1 = g1 i(j+1) -g0 i(j+1) , g1 i(j+1) is the grayscale measurement value change, g0 i(j+1) is the preset gray value change; x1 and x2 are the minimum and maximum values ​​of the jth column of the temperature measurement value change matrix; the boundary endpoints of the interval after the interval is expanded are assigned to x ij If the product is greater than 0, the current interval will continue to expand until the product of the objective function values ​​corresponding to the boundary endpoints of the current interval (x1′+x2′) is less than 0, and the current interval (x1′+x2′) is taken as x ij The corresponding maximum value range; let x0 = (x1′ + x2′) / 2, record x ij =x0 when the objective function value is recorded as L10, X i =x1′, the objective function value is recorded as L11; if L11*L10<0, let x2′=x0, otherwise let x1′=x0 to obtain the new interval (x1′′+x2″), and so on, continue to take the midpoint of the interval to gradually reduce x ij The range of the interval until the boundary endpoint of the current interval (x1″′+x2″′) is assigned x ij When the corresponding objective function value product is lower than the first minimum threshold; the current interval (x1″′+x2″′) is taken as x ij The corresponding target value range, determine x within the corresponding target value range ij Then we get the column vector X i .

[0093] The objective function is constructed as: L1 = g1 i(j+1) -g0 i(j+1) ; Among them, g1 i(j+1) is the grayscale measurement value change, g0 i(j+1) is the preset grayscale value change.

[0094] In determining x ij When x ij Too big, g0 i(j+1) <g1 i(j+1) , L1>0; if x ij Small, g0 i(j+1) >g1 i(j+1) , L1<0; when xij g1 i(j+1) ≈g0 i(j+1) , consider L1=0. Thus the problem of finding x ij is converted to the problem of finding the zero point of the objective function, which is solved by the bisection method.

[0095] The specific steps are as follows:

[0096] First, assume that x ij is located in the interval [dT min (j)dT max (j)].

[0097] Let x ij = x1corresponding to the objective function value L11, x ij = x2corresponding to the objective function value L12; if L11*L12>0, then expand the interval range to 2*[dT min (j)dT max (j)]; if the interval is expanded, the objective function value is still L11*L12>0, then continue to expand until L11*L12<0, and record the interval range as [x1, x2], considering that x ij is located in the interval [x1, x2].

[0098] Let x0=(x1+x2) / 2, and the objective function value when x ij = x0is recorded as L10; if L11*L10<0, let x2=x0, otherwise let x1=x0, and x ij is located in the interval [x1, x2]. Then continue to take the midpoint of the interval, gradually narrowing the interval range of x ij , until the interval is small enough or L10=0, and let x ij =x0.

[0099] As an optional implementation, S31 includes: setting the jth column element x i in X ij to be located in the interval 2*[x1x2], letting x0=(x1+x2) / 2 and Δx=(x2-x1) / 2; x1and x2are the minimum value and maximum value of the jth column of the temperature measurement value change matrix; construct a preset vector [x0-2Δx, x0-Δx, x0, x0+Δx, x0+2Δx]; obtain the corresponding objective function values L2=|g1 i(j+1) -g0 i(j+1) | 2 +|g1 i(2k-1-j) +g0 i(j+1) | 2 when x i(j+1) , g1 i(2k-1-j) , g1i(2k-1-j) is the grayscale measurement value change, g0 i(j+1) is the preset grayscale value change; the value corresponding to the minimum objective function value is recorded as x0, and then Δx is changed to half of the original value Δx / 2, and the preset vector corresponding to Δx / 2 is constructed to obtain x ij The corresponding objective function value when each element is equal to the new preset vector is recorded as the value corresponding to the minimum objective function value as the new x0, and so on until x ij When the corresponding objective function value is lower than the second minimum threshold, let x ij =x0, and then we get the column vector X i .

[0100] Specifically, construct the objective function and make full use of the gray value change data on both sides of the central axis:

[0101] L2=|g1 i(j+1) -g0 i(j+1) | 2 +|g1 i(2k-1-j) +g0 i(j+1) | 2

[0102] Among them, g1 i(j+1) 、g1 i(2k-1-j) is the grayscale measurement value change, g0 i(j+1) is the preset grayscale value change.

[0103] In determining x ij When x ij The farther away from the true value, the larger the L2 value; when x ij When it is extremely close to the true value, the L2 value is the minimum. ij The problem is transformed into the problem of finding the minimum value of the objective function.

[0104] The specific steps are:

[0105] First, assume that x ij In the interval 2*[dT min (j)dT max (j)], let x0=(dT min (j)+dT max (j)) / 2, Δx=(dT max (j)-dT min (j)) / 2, construct a vector of length 5 [x0-2Δx, x0-Δx, x0, x0+Δx, x0+2Δx]; x ij When they are equal to 5 values ​​respectively, find the corresponding 5 objective function values ​​and select the x with the smallest corresponding objective function value ijThe value is x0, while Δx becomes half of the original, thus constructing a new vector with length 5. By analogy, the value interval of the vector is getting smaller and smaller, gradually approaching x ij The true value, the value of the objective function is also getting smaller and smaller. When the interval is small enough, let x ij = x0.

[0106] As an optional implementation, considering the main features of the physical space, the physical constraint is set as: the radial temperature difference of the temperature corresponding to any element in the temperature true value matrix corresponding to the preset temperature value change matrix X is greater than the axial temperature difference.

[0107] The main features of the physical space include:

[0108] 1) The temperature distribution of adjacent sections of the discharge channel is similar: representing the similarity of adjacent section temperatures, from a single point, since the direction of channel expansion during the development of the discharge channel is radially outward, for any point at a certain radius, the heat conduction is mainly along the radius, i.e. the radial temperature difference is greater than the axial temperature difference. For any point in the discharge channel, the radial temperature difference is greater than the axial temperature difference. Taking the left half of the channel as an example, the temperature should satisfy the formula:

[0109] |T ij -T (i-1)j |<|T ij -T i(j-1) |,|T ij -T (i+1)j |<|T ij -T i(j-1) |,j<k;

[0110] 2) The center temperature of the channel gradually decreases in the direction away from the discharge electrode; if the center temperatures of the consecutive m sections are t1, t2…t m , linear fitting is performed using the least squares method, and theoretically the correlation coefficient k is less than or equal to 0.

[0111] 3) The temperature distribution of each section is high in the middle and low on both sides, and the temperature is roughly symmetric about the center. For any section temperature t1, t2…t n , there is a maximum value t i , satisfying:

[0112] t i ≥t i-1 ≥t i-2 ≥…≥t1,t i ≥t i+1 ≥t i+2 ≥…≥t n .

[0113] 4) The real gray value variation is caused by the temperature variation, which leads to the density variation and further affects the light deflection. The real gray value variation superimposed with the uniformly distributed noise value is the gray measurement value. The error of the gray value is caused by the schlieren camera, which has uniformity and randomness.

[0114] The following illustrates the effect simulation diagram of the method for obtaining the temperature of the discharge channel from the schlieren image based on the Abelian inverse transform provided by the application.

[0115] It is assumed that the temperature of each cross section of the discharge channel conforms to Gaussian distribution, the center temperature is 2500K, the schlieren picture is constructed and Gaussian noise with a mean value of 0 and a variance of 15 is added, as shown in Figure 6a The schlieren picture is applied to the algorithm, and only one cross section in the black frame is selected in order to speed up the running speed of the algorithm. The algorithm running result is as shown in Figure 6b 、 Figure 6c and Figure 6d . Figure 6a The temperatures of adjacent cross sections are similar, the temperature distribution of each cross section is high in the middle and low at both sides; Figure 6b The gray values of each row are similar, and the curve is smooth; Figure 6c The error of the gray value is the uniformly distributed random noise, which meets the physical constraint.

[0116] Figure 6e The temperature values of each cross section obtained by the algorithm and the real temperature values are displayed in the same coordinate, it can be directly seen that the algorithm result is very similar to the real value, and the error has little effect on the calculation result.

[0117] Figure 6f The absolute error of the temperature value of each sampling point is calculated and displayed in the three-dimensional graph, it can be seen that the temperature error is still mainly concentrated in the center area of the discharge channel, the error size is not more than 200K, and the error has little effect on the overall temperature value.

[0118] Figure 6g The relative error of the temperature value of each sampling point is calculated and displayed in the three-dimensional graph, it can be seen that the relative error is not more than 8% in this case, and it is estimated that the relative error will not exceed 15% in other cases, the error has little effect on the solution result of the temperature value, and the algorithm accuracy is high.

[0119] Example 2

[0120] The embodiment provides a device for acquiring discharge channel temperature from a striae image based on Abelian inverse transformation, comprising a configuration module, an alignment module, a determination module and a transformation module. The configuration module is used for configuring a gray scale measurement value variation matrix corresponding to a gray scale measurement value matrix of the striae image of the discharge channel; and Abelian inverse transformation is performed on each row in the gray scale measurement value variation matrix to obtain a temperature measurement value matrix. The alignment module is used for determining a central axis of the temperature measurement value matrix by using central point positions of each row of the temperature measurement value matrix; performing position alignment on the temperature measurement value matrix and the gray scale measurement value variation matrix by using the central axis; acquiring a temperature measurement value variation matrix corresponding to a part of the aligned temperature measurement value matrix on one side of the central axis, and maximum values and minimum values of each column of the temperature measurement value variation matrix. The determination module is used for determining respective target value ranges of the maximum values and the minimum values of each column of the temperature measurement value variation matrix, and sequentially determining each column vector in a preset temperature value variation matrix of the same size as the temperature measurement value variation matrix, and element values in each column vector are in the corresponding target value range. The transformation module is used for performing mirror image on a preset temperature value matrix corresponding to the preset temperature value variation matrix X by using the central axis and splicing to obtain a temperature real value matrix.

[0121] The division of each module in the device for acquiring discharge channel temperature from a striae image based on Abelian inverse transformation is only used for example, and in other embodiments, the device for acquiring discharge channel temperature from a striae image based on Abelian inverse transformation can be divided into different modules as required to complete all or part of the functions of the device for acquiring discharge channel temperature from a striae image based on Abelian inverse transformation.

[0122] The specific limitation of the device for acquiring discharge channel temperature from a striae image based on Abelian inverse transformation can be referred to the limitation of the method for acquiring discharge channel temperature from a striae image based on Abelian inverse transformation, which will not be described here. Each module in the device for acquiring discharge channel temperature from a striae image based on Abelian inverse transformation can be realized by software, hardware and a combination thereof in whole or in part. Each module can be embedded in or independent of a processor in a computer device in the form of hardware, or can be stored in a memory in the computer device in the form of software, so as to call and execute the operation corresponding to each module by the processor.

[0123] Embodiment 3

[0124] The embodiment provides an image processing device, comprising a memory and a processor, the memory stores a computer program, and the processor implements the steps of the above method when executing the computer program.

[0125] Embodiment 4

[0126] The embodiment provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to realize the steps of the method.

[0127] Those skilled in the art can understand that the above description is only the preferred embodiment of the present application, and is not used to limit the present application, and any modification, equivalent replacement and improvement made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A method for obtaining discharge channel temperature from a schlieren image based on inverse Abel transform, characterized in that: include: S1: constructing the grayscale measurement value variation matrix corresponding to the grayscale measurement value matrix of the schlieren image of the discharge channel; Performing an inverse Abel transform on each row in the grayscale measurement value variation matrix to obtain a temperature measurement value matrix; S2: Determine the central axis of the temperature measurement value matrix using the center point position of each row of the temperature measurement value matrix; aligning the temperature measurement value matrix and the grayscale measurement value variation matrix using the central axis; Obtaining a temperature measurement value variation matrix corresponding to a portion of the aligned temperature measurement value matrix on one side of the central axis, and a maximum value and a minimum value of each column of the temperature measurement value variation matrix; S3: using the maximum and minimum values ​​of each column of the temperature measurement value variation matrix to determine the corresponding target value range, and sequentially determining each column vector in a preset temperature value variation matrix of the same size as the temperature measurement value variation matrix, wherein the element value in each column vector is within the corresponding target value range; S4: The preset temperature value change matrix The corresponding preset temperature value matrix is ​​mirrored about the central axis and spliced ​​to obtain a temperature real value matrix; The grayscale measurement value variation matrix corresponding to the grayscale measurement value matrix of the discharge channel schlieren image constructed in S1 includes: A section of the discharge channel schlieren image is selected as a target schlieren image; the selection principle is as follows: a section of the discharge channel schlieren image with a vertical downward direction and no branches is selected as the target schlieren image, and the target schlieren image is selected to be as long as possible in the vertical direction and with as many grayscale value rows as possible, and the horizontal section range is selected to completely cover the discharge channel while having as few grayscale value columns as possible; Obtaining a grayscale measurement value matrix of the target schlieren image; Adjacent columns of the grayscale measurement value matrix are subtracted and used as elements of corresponding columns in the corresponding grayscale measurement value variation matrix.

2. The method for obtaining the discharge channel temperature from the schlieren image based on the inverse Abel transform according to claim 1, characterized in that: The step of obtaining a grayscale measurement value matrix of the target schlieren image includes: Each column in the original grayscale value matrix of the target schlieren image is averaged, and the number of columns closest to the central axis is recorded as o; the number of columns a with the minimum grayscale value and the number of columns b with the maximum grayscale value in each row are found; each row is intercepted with o as the center point and K* (ba) as the radius to obtain the grayscale measurement value matrix of the target schlieren image; K is a preset multiple to obtain the grayscale value matrix covering the discharge channel.

3. The method for obtaining the discharge channel temperature from the schlieren image based on the inverse Abel transform according to claim 1, characterized in that: The S3 includes: S31: Determine the target value range corresponding to each element of the preset temperature value variation matrix using the maximum and minimum values ​​of each column of the temperature measurement value variation matrix; determine the target value range corresponding to each element of the preset temperature value variation matrix within the corresponding target value range. X i The elements in S32: Detection confirmed X i Whether the temperature in the corresponding temperature true value matrix meets the physical constraints; If it does not meet the requirements, fine-tune it until it meets the physical constraints; the temperature value corresponding to the physical constraints is taken as the real X i , custom settings X k-1 , obtain a preset temperature value variation matrix of the same scale as the temperature measurement value variation matrix , where k is the total number of columns in the preset temperature value matrix.

4. The method for obtaining the discharge channel temperature from the schlieren image based on the inverse Abel transform according to claim 3, characterized in that: The S31 includes: Get interval The two boundary endpoints of X i The j-th element in the The product of the corresponding objective function values; if the product is greater than 0, the interval will be expanded ; Among them, the objective function is: , is the grayscale measurement value change, is the preset gray value change; and are the minimum and maximum values ​​of the jth column of the temperature measurement value variation matrix; Get the boundary endpoints of the interval after the interval is expanded and assign them to The product of the corresponding objective function value; if the product is greater than 0, the current interval will continue to expand until the current interval The product of the objective function values ​​corresponding to the boundary endpoints is less than 0, and the current interval As The corresponding maximum value range; make ,remember When the objective function value is recorded as L10, X i When the objective function value is recorded as L11; if Then order , otherwise let Get the new interval , and so on, continue to take the midpoint of the interval and gradually reduce it The range of the interval, up to the current interval Boundary endpoint assignment When the corresponding objective function value product is lower than the first minimum threshold; the current interval As The corresponding target value range is determined within the corresponding target value range Then we get the column vector X i .

5. The method for obtaining the discharge channel temperature from the schlieren image based on the inverse Abel transform according to claim 3, characterized in that: The S31 includes: set up X i The j-th element in the Located in the interval Between, let , ; and are the minimum and maximum values ​​of the jth column of the temperature measurement value variation matrix; Constructing a preset vector ; Get The corresponding objective function values ​​when they are equal to each element in the preset vector , 、 is the grayscale measurement value change, is the preset gray value change; The value corresponding to the minimum value of the objective function is recorded as , and then Become half of the original / 2, construction / 2 corresponding preset vector, get The corresponding objective function value when they are equal to each element in the new preset vector is recorded as the value corresponding to the minimum objective function value. , and so on until Equal to the new When the corresponding objective function value of each element in the corresponding preset vector is lower than the second minimum threshold, let , and then we get the vector X i .

6. The method for obtaining the discharge channel temperature from the schlieren image based on the inverse Abel transform according to claim 3, characterized in that: The physical constraint is: the preset temperature value change matrix The temperature corresponding to any element in the corresponding temperature true value matrix has a radial temperature difference that is greater than the axial temperature difference.

7. A device for obtaining discharge channel temperature from a schlieren image based on inverse Abel transform, characterized in that: The method for obtaining the discharge channel temperature from the schlieren image based on the inverse Abel transform according to any one of claims 1 to 6 comprises: A construction module is used to construct a grayscale measurement value variation matrix corresponding to the grayscale measurement value matrix of the discharge channel schlieren image; perform an inverse Abel transform on each row in the grayscale measurement value variation matrix to obtain a temperature measurement value matrix; an alignment module, configured to determine a central axis of the temperature measurement value matrix using the center point positions of each row of the temperature measurement value matrix; align the temperature measurement value matrix with the grayscale measurement value variation matrix using the central axis; and obtain a temperature measurement value variation matrix corresponding to a portion of the aligned temperature measurement value matrix on one side of the central axis, as well as a maximum value and a minimum value of each column of the temperature measurement value variation matrix; a determination module, configured to determine a corresponding target value range using the maximum and minimum values ​​of each column of the temperature measurement value variation matrix, and sequentially determine each column vector in a preset temperature value variation matrix of the same size as the temperature measurement value variation matrix, wherein the element value in each column vector is within the corresponding target value range; A transformation module is used to transform the preset temperature value change matrix The corresponding preset temperature value matrix is ​​mirrored about the central axis and spliced ​​to obtain a temperature real value matrix.

8. An image processing device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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