A method for extracting moire fringe phase information based on Morlet wavelet transform

Abstract

This invention discloses a method for extracting moiré fringe phase information based on Morlet wavelet transform, comprising: converting a target moiré fringe image into a grayscale image; filtering the grayscale image to obtain a filtered binarized image; performing mathematical morphological denoising on the binarized image to obtain a processed image, wherein the mathematical morphological denoising includes erosion and dilation; convolving each column of the processed image using modulated Morlet wavelets and calculating the amplitude and phase of the wavelet coefficients; determining wavelet ridges based on the amplitude of the wavelet coefficients and extracting the phase of the scale coefficients and time coefficients corresponding to the wavelet ridge positions; and obtaining complete moiré fringe phase information based on the phases of all extracted columns. This method is highly accurate and easy to implement, making it suitable for further refractive index reconstruction and key parameter measurement of the measured flow field.

Description

Technical Field

[0001] This invention relates to a method for extracting moiré fringe phase information based on Morlet wavelet transform, belonging to the field of optical measurement technology. Background Technology

[0002] Moiré tomography, a branch of optical computational tomography, offers advantages such as real-time processing, stability, and non-contact operation, making it widely applicable in flow field detection. When using moiré tomography to measure key parameters of complex high-temperature flow fields, ensuring measurement accuracy requires maximizing the precision of fringe phase information extraction. Currently, Fourier transform is more commonly used in practical measurements for extracting moiré fringe phase information.

[0003] Therefore, finding a simpler and more accurate method for extracting fringe phase information is of great significance for the application of moiré tomography in the field of flow field measurement. Summary of the Invention

[0004] Objective: To overcome the shortcomings of existing technologies, this invention provides a method for extracting moiré fringe phase information based on Morlet wavelet transform, which is highly accurate and easy to implement, so as to be used for further refractive index reconstruction and key parameter measurement of the measured flow field.

[0005] Technical solution: To solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0006] In a first aspect, the present invention provides a method for extracting moiré fringe phase information based on Morlet wavelet transform, comprising:

[0007] Convert the target moiré fringe image to a grayscale image;

[0008] The grayscale image is filtered to obtain a filtered binarized image;

[0009] The binary image is subjected to mathematical morphological denoising to obtain the processed image, wherein the mathematical morphological denoising includes erosion and dilation;

[0010] The modulated Morlet wavelet is used to convolve each column of the processed image, and the amplitude and phase of the wavelet coefficients are calculated.

[0011] The wavelet ridge is determined based on the amplitude of the wavelet coefficients, and the phase of the scale coefficient and time coefficient corresponding to the position of the wavelet ridge is extracted.

[0012] Based on the phase of all extracted columns, complete moiré fringe phase information is obtained.

[0013] In some embodiments, converting the target moiré fringe image into a grayscale image includes: assigning a matrix of grayscale values ​​from 0 to 1 to each pixel in the target moiré fringe image.

[0014] In some embodiments, filtering the grayscale image includes: denoising the grayscale image using Gaussian filtering, specifically including:

[0015] A K×K Gaussian kernel is used to smooth the grayscale image I(x,y), wherein the Gaussian kernel G(i,j) is denoted as:

[0016]

[0017] Where i and j are offsets relative to the center pixel position, and σ is the standard deviation of the Gaussian distribution;

[0018] When traversing all pixels (x,y) of the grayscale image, a Gaussian kernel G(i,j) is applied to all pixels in the K×K neighborhood centered at (x,y), resulting in the new output pixel value O(x,y) as shown below:

[0019]

[0020] Where K represents the neighborhood of pixels selected for calculating the weighted average gray value in image smoothing operations;

[0021] Gaussian filtering uses convolutional neural networks or mask neural networks to scan each pixel in a grayscale image and use the weighted average grayscale value as the value of the center pixel of the template, thereby optimizing the grayscale image.

[0022] In some embodiments, mathematical morphological denoising of the binarized image includes removing noise from the binarized image through erosion and dilation operations of opening.

[0023] Furthermore, in some embodiments, each column of the processed image is convolved using modulated Morlet wavelets, including:

[0024]

[0025] Where f(x) is any column of the light intensity distribution I(x,y) of the moiré fringe image, and W f (a, b) represent the corresponding columns of the convolved image, M * a,b (x) is the Morlet wavelet transform mother function. The complex conjugate function, where a and b are the scaling and time parameters of the mother wavelet, respectively.

[0026] Furthermore, in some embodiments, calculating the amplitude A(a,b) and phase φ(a,b) of the wavelet coefficients includes:

[0027]

[0028]

[0029] Where Im(W) f (a,b)), Re(W) f (a, b) are complex numbers W f The imaginary and real parts of (a,b).

[0030] In some embodiments, wavelet ridges are determined based on the amplitudes of the wavelet coefficients, and the phase of the scale coefficient and time coefficient corresponding to the position of the wavelet ridges is extracted, including:

[0031] The ridge of the wavelet is selected at the local maximum of the amplitude of the wavelet coefficient. The ridges of the wavelets are connected to form the wavelet ridge line. The phase of the corresponding scale coefficient and time coefficient at the position of the wavelet ridge line is the phase of the light intensity distribution of that column in the moiré fringe image.

[0032] In a second aspect, the present invention provides a device for extracting moiré fringe phase information based on Morlet wavelet transform, including a processor and a storage medium;

[0033] The storage medium is used to store instructions;

[0034] The processor is configured to operate according to the instructions to execute the method according to the first aspect.

[0035] Thirdly, the present invention provides an apparatus comprising,

[0036] Memory;

[0037] processor;

[0038] as well as

[0039] Computer programs;

[0040] The computer program is stored in the memory and configured to be executed by the processor to implement the method described in the first aspect above.

[0041] Fourthly, the present invention provides a storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in the first aspect.

[0042] Beneficial effects: The method for extracting moiré fringe phase information based on Morlet wavelet transform provided by this invention has high accuracy and is easy to implement, so as to be used for further refractive index reconstruction and key parameter measurement of the measured flow field. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the experimental apparatus according to an embodiment of the present invention;

[0044] Figure 2 The image is a grayscale image after grayscale processing according to an embodiment of the present invention, wherein (a) is an image before burning and (b) is an image after burning;

[0045] Figure 3 This is a schematic diagram of a stripe pattern obtained after Gaussian filtering and mathematical morphology operations according to an embodiment of the present invention.

[0046] Figure 4 This is a schematic diagram of the phase information of a candle flame combustion field obtained by extracting and subtracting the phase information of moiré fringes with and without combustion according to an embodiment of the present invention.

[0047] Figure 1 In the middle: 1-Laser; 2, 3-Beam expanding and collimating system; 4-Field to be measured; 5, 6-Ronchi grating; 7, 9-Imaging lens; 8-Filter; 10-Receiving screen. Detailed Implementation

[0048] The present invention will be further described below with reference to the accompanying drawings and embodiments. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention, and should not be used to limit the scope of protection of the present invention.

[0049] In the description of this invention, "several" means one or more, "multiple" means two or more, "greater than," "less than," and "exceeding" are understood to exclude the stated number, while "above," "below," and "within" are understood to include the stated number. The use of "first" and "second" in the description is merely for distinguishing technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the order of the indicated technical features.

[0050] In the description of this invention, the terms "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0051] Example 1

[0052] Firstly, this embodiment provides a method for extracting moiré fringe phase information based on Morlet wavelet transform, including:

[0053] S1) Convert the target moiré fringe image into a grayscale image;

[0054] S2) Filter the grayscale image to obtain a filtered binarized image;

[0055] S3) Perform mathematical morphological denoising on the binarized image to obtain the processed image, wherein the mathematical morphological denoising includes erosion and dilation;

[0056] S4) Convolve each column of the processed image using modulated Morlet wavelets and calculate the amplitude and phase of the wavelet coefficients;

[0057] S5) Determine the wavelet ridge line based on the amplitude of the wavelet coefficients, and extract the phase of the scale coefficient and time coefficient corresponding to the position of the wavelet ridge line;

[0058] S6) Based on the phase of all extracted columns, obtain the complete moiré fringe phase information.

[0059] In some embodiments, S1) converting the target moiré fringe image into a grayscale image includes: assigning a matrix of grayscale values ​​from 0 to 1 to each pixel in the target moiré fringe image.

[0060] In some embodiments, S2) filtering the grayscale image includes: using Gaussian filtering to reduce noise in the grayscale image, specifically including:

[0061] A K×K Gaussian kernel is used to smooth the grayscale image I(x,y), wherein the Gaussian kernel G(i,j) is denoted as:

[0062]

[0063] Where i and j are offsets relative to the center pixel position, and σ is the standard deviation of the Gaussian distribution; note that this Gaussian kernel has been normalized, so the sum of the convolution results is in the same range as the original pixel values.

[0064] When traversing all pixels (x,y) of the grayscale image, a Gaussian kernel G(i,j) is applied to all pixels in the K×K neighborhood centered at (x,y), resulting in the new output pixel value O(x,y) as shown below:

[0065]

[0066] Where K represents the neighborhood of pixels selected for calculating the weighted average gray value in image smoothing operations;

[0067] Gaussian filtering uses convolutional neural networks or mask neural networks to scan each pixel in a grayscale image and use the weighted average grayscale value as the value of the center pixel of the template, thereby optimizing the grayscale image.

[0068] In some embodiments, S3), mathematical morphological denoising of the binarized image includes removing noise from the binarized image through erosion and dilation operations of opening.

[0069] Erosion is a technique that eliminates boundary points of an object; it effectively removes all objects smaller than the target structural element. aΘb represents the erosion of a by b, specifically defined as:

[0070]

[0071] Here, aΘb can be regarded as the set of all x that make b, after being translated by x, contained in a.

[0072] The effect of expansion is to enlarge the target area, fill the gaps inside the object, and thus connect two objects that are close to each other. This represents the expansion of a by b, specifically defined as:

[0073]

[0074] The steps of dilation are: first, b performs a mapping about the origin, then translates x, and then dilates. After being translated by x, it will result in it having at least one non-zero common element with a.

[0075] The regions with obvious changes in the stripes of the obtained edge image are extracted, and the appropriately sized and high-quality images are then subjected to row and column convolution of the moiré stripe image using modulated Morlet wavelets.

[0076] In some embodiments, S4), convolving each column of the processed image using modulated Morlet wavelets includes:

[0077]

[0078] Where f(x) is any column of the light intensity distribution I(x,y) of the moiré fringe image, and W f (a, b) represent the corresponding columns of the convolved image, M * a,b (x) is the Morlet wavelet transform mother function. The complex conjugate function, where a and b are the scaling and time parameters of the mother wavelet, respectively.

[0079] In some embodiments, S4), the amplitude A(a,b) and phase φ(a,b) of the wavelet coefficients are calculated:

[0080]

[0081]

[0082] Where Im(W) f (a,b)), Re(W) f (a, b) are complex numbers W f The imaginary and real parts of (a,b).

[0083] In some embodiments, S5), the wavelet ridge is determined based on the amplitude of the wavelet coefficients, and the phase of the scale coefficient and time coefficient corresponding to the position of the wavelet ridge is extracted, including:

[0084] The ridge of the wavelet is selected at the local maximum of the amplitude of the wavelet coefficient. The ridges of the wavelets are connected to form the wavelet ridge line. The phase of the corresponding scale coefficient and time coefficient at the position of the wavelet ridge line is the phase of the light intensity distribution of that column of the moiré fringe image (the phase with the best wavelet fitting quality).

[0085] In some embodiments, S6) based on the phases of all extracted columns, complete moiré fringe phase information is obtained, specifically including:

[0086] For each column of the light intensity distribution in the moiré fringe image, the same method, namely convolution, is used to calculate the amplitude and phase of the wavelet coefficients, find the wavelet ridges, and extract the phase. Finally, integrating these methods yields the complete phase information.

[0087] In some embodiments, a method for extracting moiré fringe phase information based on Morlet wavelet transform includes:

[0088] The experimental apparatus used in this embodiment follows the principle as follows: Figure 1 As shown. G1 and G2 are a pair of Ronchi gratings with a grating constant of d and a grating spacing of Δ. To obtain better fringe contrast, Δ should satisfy the Talbot distance, i.e., Δ = jd. 2 / λ, the grating lines of the two gratings form angles of +α / 2 and -α / 2 with the y-axis, respectively. The path from the back of grating G2 to the receiving screen 10 is a typical 4-f system. Utilizing Figure 1 The device can obtain moiré fringes of the measured flow field. The moiré fringes are acquired using a CCD and transmitted to a computer for phase information extraction. This patent uses a candle flame as the measured flow field for experimental demonstration, proving the feasibility of this phase information extraction method.

[0089] Example: A candle flame combustion field experiment, with the moiré fringe images collected during the experiment. Figure 2 (a) Moiré fringe image before combustion and (b) Moiré fringe image after combustion.

[0090] Figure 2 The images are grayscale images after grayscale processing, where (a) is the image before burning and (b) is the image after burning.

[0091] In the images obtained from the experiment ( Figure 2 After performing Gaussian filtering and mathematical morphology operations, the result is... Figure 3 The stripe pattern shown is clear. Figure 3 The box in the diagram represents the effective area for phase extraction.

[0092] In this example, the phase information of the candle flame combustion field is obtained by extracting the phase information of the moiré fringes with and without combustion, and then subtracting them. The result is as follows. Figure 4 As shown.

[0093] Example 2

[0094] Secondly, based on Embodiment 1, this embodiment provides a device for extracting moiré fringe phase information based on Morlet wavelet transform, including a processor and a storage medium;

[0095] The storage medium is used to store instructions;

[0096] The processor is configured to operate according to the instructions to execute the method according to Embodiment 1.

[0097] Example 3

[0098] Thirdly, based on Embodiment 1, this embodiment provides a device, including,

[0099] Memory;

[0100] processor;

[0101] as well as

[0102] Computer programs;

[0103] The computer program is stored in the memory and configured to be executed by the processor to implement the method described in Embodiment 1.

[0104] Example 4

[0105] Fourthly, based on Embodiment 1, this embodiment provides a storage medium on which a computer program is stored, and when the computer program is executed by a processor, it implements the method described in Embodiment 1.

[0106] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0107] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0108] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0109] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0110] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for extracting the phase information of Moire fringes based on Morlet wavelet transform, characterized in that, The method comprises: Converting a target Moire fringe image into a gray-scale image; Filtering the gray-scale image to obtain a filtered binary image; Performing mathematical morphology noise reduction processing on the binary image to obtain a processed image, wherein the mathematical morphology noise reduction processing comprises erosion and dilation; Convolving each column of the processed image using a modulated Morlet wavelet, and calculating the amplitude A(a, b) and phase φ(a, b) of the wavelet coefficient; where f(x) is an arbitrary column of the light intensity distribution I(x,y) of the Moire fringe image, W f (a,b) is the corresponding column of the convolved image, M * a,b (x) is the Morlet wavelet transform mother function the complex conjugate function of which is where a and b are the scale and time parameters of the mother wavelet, respectively. where Im(W f (a,b)) and Re(W f (a,b)) are the imaginary and real parts of the complex W f (a,b), respectively. Determining a wavelet ridge line according to the amplitude of the wavelet coefficient, and extracting the phase of the scale coefficient and the time coefficient corresponding to the wavelet ridge line position, comprising: selecting the local maximum value of the amplitude of the wavelet coefficient as the ridge of the wavelet, and connecting the ridges of the wavelets to form a wavelet ridge line, and taking the phase of the scale coefficient and the time coefficient corresponding to the wavelet ridge line position as the phase of the column of the Moire fringe image light intensity distribution; Obtaining complete Moire fringe phase information according to the phases of all columns extracted.

2. The method of claim 1, wherein, Converting a target Moire fringe image into a gray-scale image comprises: converting a matrix of 0 to 1 gray-scale values corresponding to each pixel point in the target Moire fringe image.

3. The method of claim 1, wherein, Filtering the gray-scale image comprises: using Gaussian filtering to reduce noise of the gray-scale image, specifically comprising: Using a K×K Gaussian kernel to smooth the gray-scale image I(x, y), the Gaussian kernel G(i, j) is expressed as: Wherein, i and j are offsets relative to the center pixel position, and σ is the standard deviation of the Gaussian distribution; When traversing all pixels (x, y) of the gray-scale image, the Gaussian kernel G(i, j) is applied to all pixels in the K×K neighborhood centered at (x, y) to obtain a new output pixel value O(x, y) as follows: Wherein K is the domain range of the pixel point selected for calculating the weighted average gray-scale value in the smoothing image operation; The Gaussian filtering uses a convolutional neural network or a mask neural network to scan each pixel in the gray-scale image and takes the weighted average gray-scale value as the value of the template center pixel point, thereby realizing optimization of the gray-scale image.

4. The method of claim 1, wherein, The mathematical morphology noise reduction processing on the binary image comprises removing noise points in the binary image through erosion and dilation of the open operation.

5. A Morlet wavelet transform-based Mordeau phase information extraction apparatus characterized by comprising: Comprise a processor and a storage medium; The storage medium is used to store instructions; The processor is used to operate according to the instructions to execute the method according to any one of claims 1 to 4.

6. An apparatus, comprising: Comprise: A memory; A processor; And A computer program; Wherein, the computer program is stored in the memory and is configured to be executed by the processor to realize the method as claimed in any one of claims 1 to 4.

7. A storage medium, characterized by A computer program is stored on the storage medium, and the computer program is executed by the processor to realize the method as claimed in any one of claims 1 to 4.

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