Image enhancement method for plank surface defect detection task
By analyzing the periodic characteristics of the surface texture of the wooden board and designing an adaptive filter mask, the problem of difficult to balance the texture weakening and defect highlighting in the prior art is solved, and the accuracy and robustness of the detection of surface defects of wooden boards is improved.
Patent Information
- Application Number
- CN202510211624.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-25
- Publication Date
- 2025-06-13
- Estimated Expiration
- 2045-02-25
AI Technical Summary
The prior art is difficult to effectively balance the texture weakening and defect highlighting in the detection of wooden board surface defects, resulting in insufficient accuracy and reliability of defect detection.
By analyzing the periodic characteristics of the surface texture of the wooden board, an adaptive filter mask is designed, and the frequency components of the image are separated by Fourier transform, so as to weaken the texture information and highlight the defect characteristics.
It improves the accuracy and robustness of the detection of surface defects in wooden boards, provides more valuable image information, and facilitates subsequent defect classification and identification.
Smart Images

Figure CN120147142A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of image processing, and specifically to an image enhancement method for the task of detecting defects on the surface of wooden boards. Background Art
[0002] In industries such as wood processing and furniture manufacturing, the detection of the surface quality of wooden boards is crucial for ensuring product quality and improving production efficiency. With the continuous development of computer vision technology, using image processing technology to automatically detect defects on the surface of wooden boards has become a new direction. Image processing technology can automatically identify and locate defect areas by analyzing and processing the images of the wooden board surface, thereby achieving fast and accurate defect detection. In recent years, deep learning methods have been increasingly used for the task of detecting defects on the surface of wooden boards. By constructing multi-layer neural networks, deep learning can automatically learn the features in images, thereby achieving accurate recognition and location of targets. However, the performance of deep learning models depends to a large extent on the quality of the input images. For the task of detecting defects on the surface of wooden boards, due to the complex and diverse textures on the wooden board surface, the defect features are often not obvious, which poses a great challenge to automatic detection.
[0003] Existing image processing methods have some limitations in the detection of defects on the surface of wooden boards. Most of these image enhancement techniques rely on general image processing algorithms. When dealing with defects on the surface of wooden boards, it is often difficult to balance the relationship between texture weakening and defect highlighting. Excessive texture weakening may lead to the weakening of defect information, while excessive emphasis on defects may make the texture a disturbing factor. For example, although some image enhancement methods can improve the contrast and clarity of images to a certain extent, they are often difficult to effectively highlight the complex textures and tiny defect features on the surface of wooden boards; some image processing methods based on filtering may filter out some defect information while removing noise, resulting in a decrease in the accuracy of defect detection.
[0004] Therefore, there is an urgent need for an image enhancement method specifically for the task of detecting defects on the surface of wooden boards, which can effectively highlight the defect features on the surface of wooden boards while weakening the texture, provide high-quality image input for subsequent defect detection algorithms, thereby improving the accuracy and reliability of detecting defects on the surface of wooden boards, realizing automatic and intelligent detection of the surface quality of wooden boards, and promoting the development of industries such as wood processing and furniture manufacturing. Summary of the Invention
[0005] The technical problem to be solved by the present invention is to provide an image enhancement method for the task of detecting defects on the surface of wooden boards in view of the above-mentioned prior art. The image enhancement method for the task of detecting defects on the surface of wooden boards improves the signal-to-noise ratio and contrast of the wooden board image through image enhancement technology, making it more suitable for input into a deep learning model, so as to achieve accurate detection of defects on the surface of wooden boards. Different from traditional methods, the present invention not only considers basic attributes such as the overall contrast and brightness of the image, but also deeply analyzes the characteristic differences between the texture of the wooden board and the defects in the frequency domain. By performing Fourier transform on the grayscale image, the frequency components of the image can be separated, and then precise control of the texture and defects can be achieved. An adaptive filtering mask is also designed to effectively highlight the surface defects while weakening the texture. This method can not only improve the accuracy and robustness of defect detection, but also provide more valuable image information for subsequent defect classification and recognition.
[0006] To achieve the above technical objectives, the technical solution adopted by the present invention is as follows:
[0007] An image enhancement method for the task of detecting defects on the surface of wooden boards, including:
[0008] Step 1: Receive the input grayscale image img_gray of the wooden board surface, and obtain the number of rows rows and the number of columns cols of the image, providing basic data for subsequent processing;
[0009] Step 2: Analyze the texture characteristics of the grayscale image of the wooden board surface: Randomly select several rows in the image, perform fast Fourier transform on each row of data, calculate the normalized single-sided spectrum of the frequency-domain signal, and find the first maximum point; Record the positions of the first maximum points corresponding to each row, calculate the average value of the positions of all the first maximum points, and round down to obtain the key parameter avg_floor; This parameter reflects the periodic characteristics of the texture on the surface of the wooden board and provides a basis for subsequent filter design;
[0010] Step 3: Perform two-dimensional fast Fourier transform on the grayscale image of the wooden board surface to obtain a frequency-domain image; Center the frequency-domain image to obtain fshift; Facilitate subsequent automatic observation and analysis of the frequency distribution characteristics of the image, as well as subsequent corresponding processing in the frequency domain of the image;
[0011] Step 4: Design a filter mask mask for weakening the texture of the wooden board according to the avg_floor parameter obtained in Step 2. The mask is set to 0 within a specific range in the frequency domain to filter out specific frequency components of the texture on the wooden board surface, and the other parts are set to 1 to retain the frequency components of the defects. Weaken the texture on the wooden board surface to highlight surface defects. The width of the filtering area is maskwidth, and the filtering areas on both sides extend masklengtha and masklengthb pixels from the center to the left and right respectively, where masklengtha is set to the avgfloor parameter obtained in Step 2 and masklengthb is a fixed value. Multiply the mask mask by fshift to obtain the filtered frequency domain image fshiftwithMask.
[0012] Step 5: Perform inverse centering processing on the filtered frequency domain image fshiftwithMask to obtain fishift. Perform two-dimensional inverse fast Fourier transform on fishift to obtain the enhanced image img_back. This image highlights the defect features on the wooden board surface while retaining texture details, facilitating accurate identification by subsequent defect detection algorithms.
[0013] Step 6: Return the enhanced image img_back as the input for the wooden board surface defect detection task to improve the performance of defect detection.
[0014] As a further improved technical solution of the present invention, Step 2 is specifically as follows:
[0015] 2.1 Randomly select the row index of the grayscale image img_gray matrix on the wooden board surface. The row index is less than the number of rows rows and greater than 0. Obtain all the grayscale values in the row where the row index is located and save them as a sequence y.
[0016] 2.2 Perform fast Fourier transform (FFT) on each row of data y to convert the time-domain signal into a frequency-domain signal, obtaining the corresponding frequency-domain signal fft_y for each row. Among them, FFT is an existing efficient algorithm for calculating the discrete Fourier transform (DFT), which can quickly convert the signal from the time domain to the frequency domain for facilitating the analysis of the frequency components of the signal.
[0017] 2.3 Calculate the normalized single-sided spectrum of the frequency-domain signal, specifically as follows:
[0018] Calculate the absolute value of the frequency-domain signal fft_y to obtain the bilateral spectrum. Then divide the spectrum value by the total number of columns cols for normalization processing. Since the FFT result is symmetric, only half of the spectrum needs to be taken for analysis. Take the spectrum values in the first half to obtain the normalized single-sided spectrum normalizationhalf_y.
[0019] 2.4. Find the maximum point in the normalized single-sided spectrum normalizationhalf_y, and record the position of the first maximum point, that is, save the index value argrelmax_index of the normalizationhalf_y spectrum sequence corresponding to the first maximum point.
[0020] 2.5. Record the position argrelmax_index of the first maximum point corresponding to the row where the randomly selected row index is located, calculate the average value of all argrelmax_index, and round down to obtain the key parameter avg_floor. This parameter reflects the periodic characteristics of the wood board surface texture and will be used to design a filter in the subsequent steps to effectively highlight the defect characteristics and improve the accuracy and reliability of defect detection.
[0021] As a further improved technical solution of the present invention, step 4 is specifically as follows:
[0022] 4.1. Create a mask mask with the same size as the input image, and initialize all its elements to 1, that is, create a two-dimensional array matrix mask with all elements being 1, the number of rows being rows, and the number of columns being cols; by setting specific areas of the mask to 0 in the subsequent steps, the frequency components of these areas can be filtered out, which is used to selectively retain or filter specific frequency components.
[0023] 4.2. Set relevant parameters: Since the frequency-domain image is centered in step 3, the center of the spectrum is moved to the center position of the image. Therefore, take half of the number of rows rows as crow and half of the number of columns cols as ccol. crow and ccol respectively represent the indices of the center row and center column of the frequency-domain image; the width of the filtering area is maskwidth; masklengtha is set to the avg_floor parameter obtained in step 2; masklengthb is a fixed value; maskwidth and masklength_b can be appropriately adjusted according to the actual situation.
[0024] 4.3. Near the center row of the frequency-domain image, define the vertical range of the filter as the row range from crow - maskwidth to crow + maskwidth; on the right side of the center column of the frequency-domain image, define the horizontal range of the filter as the column range from ccol + masklengtha to ccol + masklengthb; on the left side of the center column of the frequency-domain image, define the horizontal range of the filter as the column range from ccol - masklengthb to ccol - masklengtha; set the values of the mask mask within the above range areas to 0, thereby constructing the required filter mask mask.
[0025] 4.4 Apply the filter mask mask constructed in step 4.3 to the centered frequency-domain image fshift, specifically: Multiply fshift element-wise with the filter mask mask constructed in step 4.3 to obtain the filtered frequency-domain image fshiftwithMask. By element-wise multiplication, the mask is applied to the frequency-domain image to filter out specific frequency components of the wood board surface texture and retain the wood board surface defect components.
[0026] The beneficial effects of the present invention are as follows:
[0027] (1) By analyzing the periodic characteristics of the wood board surface texture, the present invention designs a corresponding filter to effectively filter out texture information and highlight defect features. While weakening the texture detail information on the wood board surface, the defect features on the wood board surface are retained. This makes the defects more obvious in the image, facilitating accurate identification by subsequent defect detection algorithms and improving the accuracy of defect detection.
[0028] (2) The method of the present invention is applicable to wood board surface images with different textures and different defect types, and has strong generality and adaptability. Whether it is annual rings, wood grains or other complex textures, this method can effectively process them and is applicable to various types of wood board surface defect detection tasks.
[0029] (3) The method of the present invention is not only applicable to traditional image processing algorithms, but can also be used as a preprocessing step for object detection tasks based on deep learning. By improving the quality of the input image, the performance of the deep learning model is further improved, making it more accurate and efficient in processing defect detection under complex texture backgrounds.
[0030] (4) The method of the present invention is based on common image processing techniques and Fourier transform, and is easy to implement and integrate into existing detection systems. It does not require complex hardware equipment or high computing costs, and has high practicality and economy.
[0031] (5) The technical problems solved by the present invention include: In the existing wood board surface defect detection, due to the complex and diverse textures on the wood board surface, the defect features are not obvious. The existing image enhancement methods have different effects on different types of defects, and may even have the opposite effect, affecting the accuracy and reliability of defect detection; In addition, although deep learning performs well in object detection tasks, its performance depends to a large extent on the quality of the input image, and the existing methods fail to effectively improve the quality of wood board surface defect images in the preprocessing stage, thus limiting the application effect of deep learning models in wood board surface defect detection.
[0032] (6) The present invention proposes an image enhancement method specifically for the task of detecting surface defects on wooden boards. This method improves the signal-to-noise ratio and contrast of the wooden board images through image enhancement techniques, making them more suitable for input into deep learning models, thereby achieving accurate detection of surface defects on wooden boards. Different from traditional methods, the present invention not only considers basic attributes such as the overall contrast and brightness of the image, but also deeply analyzes the characteristic differences between the texture and defects of the wooden board in the frequency domain. By performing Fourier transform on the grayscale image, the present invention can separate the frequency components of the image, and then achieve precise control of the texture and defects. On this basis, the present invention designs an adaptive filtering mask that can dynamically adjust the filtering parameters according to the texture characteristics of different wooden board images, thereby effectively highlighting the surface defects while weakening the texture. This method can not only improve the accuracy and robustness of defect detection, but also provide more valuable image information for subsequent defect classification and recognition. Description of the Drawings
[0033] Figure 1 is the original surface grayscale image of the wooden board with surface defects.
[0034] Figure 2 is the frequency domain image obtained by performing two-dimensional fast Fourier transform on the entire wooden board surface grayscale image and performing centering processing.
[0035] Figure 3 is the filter mask image.
[0036] Figure 4 is the filtered frequency domain image.
[0037] Figure 5 is the wooden board image after image enhancement. Detailed Embodiment
[0038] The following further describes the detailed embodiment of the present invention with reference to the drawings:
[0039] In the existing detection of surface defects on wooden boards, due to the complex and diverse textures on the wooden board surface, the defect features are not obvious. The existing image enhancement methods have different effects on different types of defects, and may even have the opposite effect, affecting the accuracy and reliability of defect detection. In addition, although deep learning performs well in object detection tasks, its performance depends to a large extent on the quality of the input image, and the existing methods fail to effectively improve the quality of the wooden board surface defect images in the preprocessing stage, thus limiting the application effect of deep learning models in the detection of surface defects on wooden boards.
[0040] In view of the above problems, this embodiment proposes an image enhancement method specifically for the task of detecting surface defects of wooden boards. Through image enhancement technology, this method improves the signal-to-noise ratio and contrast of wooden board images, making them more suitable for input into deep learning models, thereby achieving accurate detection of surface defects of wooden boards. Different from traditional methods, this embodiment not only considers basic attributes such as the overall contrast and brightness of the image, but also deeply analyzes the characteristic differences between the texture of the wooden board and the defects in the frequency domain. By performing Fourier transform on the grayscale image, this embodiment can separate the frequency components of the image, and then achieve precise control of the texture and defects. On this basis, this embodiment designs an adaptive filtering mask that can dynamically adjust the filtering parameters according to the texture characteristics of different wooden board images, thereby effectively highlighting the surface defects while weakening the texture. This method can not only improve the accuracy and robustness of defect detection, but also provide more valuable image information for subsequent defect classification and recognition. Specifically, an image enhancement method for the task of detecting surface defects of wooden boards includes:
[0041] Step 1: Receive the input grayscale image img_gray of the wooden board surface (as Figure 1 shown), obtain the number of rows rows and the number of columns cols of the image, and provide basic data for subsequent processing.
[0042] Step 2: Automatically analyze the texture characteristics of the wooden board. Randomly select 5 rows in the image, perform fast Fourier transform (FFT) on each row of data, calculate the normalized single-sided spectrum of the frequency-domain signal, and find the first maximum point. Record the positions of the first maximum points corresponding to each row, calculate the average value of these positions, and round down to obtain the key parameter avg_floor, which reflects the periodic characteristics of the wooden board surface texture and provides a basis for subsequent filter design.
[0043] Step 3: Perform two-dimensional fast Fourier transform on the entire grayscale image of the wooden board surface to obtain the frequency-domain image f. Center the frequency-domain image to obtain fshift (as Figure 2 shown), which is convenient for subsequent automatic observation and analysis of the frequency distribution characteristics of the image, as well as subsequent corresponding processing in the image frequency domain.
[0044] Step 4: According to the avg_floor parameter obtained in Step 2, design a filter mask mask for weakening the texture of the wooden board (as Figure 3As shown). The mask is set to 0 within a specific range in the frequency domain to filter out specific frequency components of the texture on the wooden board surface, and the other parts are set to 1 to retain the frequency components of the defects. The texture on the wooden board surface is weakened, thereby highlighting the surface defects. The width of the filtering area is maskwidth, and the filtering areas on both sides extend masklengtha and masklengthb pixels respectively from the center to the left and right, where masklengtha is set to the avg_floor parameter obtained in step 2, and masklengthb is a fixed value. Multiply the designed mask mask by fshift to obtain the filtered frequency domain image fshiftwithMask (as Figure 4 shown).
[0045] Step 5: Perform inverse centering processing on the filtered frequency domain image fshiftwithMask to obtain fishift. Perform two-dimensional inverse fast Fourier transform on fishift to obtain the enhanced image img_back (as Figure 5 shown). While retaining the texture details, this image highlights the defect features on the wooden board surface, facilitating accurate identification by subsequent defect detection algorithms.
[0046] Step 6: Return the enhanced image img_back as the input for the wooden board surface defect detection task to improve the performance of defect detection.
[0047] The specific steps of step 2 are as follows:
[0048] 2.1 Randomly select 5 rows from the grayscale image of the wooden board surface. The selection of these rows is random to ensure the representativeness and generalization ability of the analysis results. That is, randomly select the row indices of the img_gray matrix of the grayscale image of the wooden board surface. The row index is less than the number of rows rows and greater than 0, obtain all the grayscale values of the row where the row index is located, and save them as the sequence y.
[0049] 2.2 Perform fast Fourier transform (FFT) on each row of data y to convert the time-domain signal into a frequency-domain signal, obtaining the frequency-domain signal fft_y of that row. Among them, FFT is an existing efficient algorithm for calculating the discrete Fourier transform (DFT), which can quickly convert the signal from the time domain to the frequency domain, facilitating the analysis of the frequency components of the signal.
[0050] 2.3 Calculate the normalized single-sided spectrum of the frequency-domain signal. Specifically, calculate the absolute value of the frequency-domain signal fft_y to obtain the two-sided spectrum. Then divide the spectrum values by the total number of columns cols for normalization processing. Since the FFT result is symmetric, only half of the spectrum needs to be taken for analysis. Take the spectrum values of the first half to obtain the normalized single-sided spectrum normalizationhalf_y.
[0051] 2.4. The texture on the surface of the wooden board usually has a certain periodicity, such as annual rings, wood grain, etc. These periodic textures are manifested as peaks at specific frequencies in the frequency domain. In the frequency domain, periodic textures usually correspond to low-frequency components. By finding the first maximum point, the dominant frequency of these periodic textures can be determined. This dominant frequency reflects the periodic characteristics of the texture, such as the spacing or repetition frequency of the texture. Therefore, finding the first maximum point of the unilateral spectrum can be used for subsequent steps to determine the range of low-frequency components that need to be filtered out. The specific steps are to find the maximum point in the normalization half-spectrum normalizationhalf_y and record the position of the first maximum point, that is, save the index value argrelmax_index of the normalizationhalf_y spectrum sequence corresponding to the first maximum point.
[0052] 2.5. Record the positions argrelmax_index of the first maximum points corresponding to all 5 random rows, calculate the average value of these 5 argrelmax_index values, and round down to obtain the key parameter avg_floor. This parameter reflects the periodic characteristics of the texture on the surface of the wooden board and will be used for subsequent filter design to effectively highlight the defect characteristics and improve the accuracy and reliability of defect detection.
[0053] The specific content of step 4 is as follows:
[0054] 4.1. Create a mask mask with the same size as the input image, and initialize all its elements to 1, that is, create a two-dimensional array matrix mask with all elements being 1, the number of rows being rows, and the number of columns being cols. By setting specific areas of the mask to 0 in subsequent steps, the frequency components of these areas can be filtered out, which is used to selectively retain or filter out specific frequency components.
[0055] 4.2. Set relevant parameters. Since the frequency-domain image is centered in step 3, the center of the spectrum is moved to the center position of the image. Therefore, take half of the number of rows rows as crow and half of the number of columns cols as ccol. crow and ccol respectively represent the indices of the center row and center column of the frequency-domain image. The width maskwidth of the filtering area is default set to 5; masklengtha is set to the avg_floor parameter obtained in step 2; masklengthb is default set to 400, where the default value 400 is considered to be sufficient to filter out the periodic characteristics of the texture on the surface of the wooden board. maskwidth and masklengthb can be adjusted appropriately according to the actual situation.
[0056] 4.3. Near the central row of the frequency-domain image, define the vertical range of the filter as the row range from crow-maskwidth to crow+maskwidth; on the right side of the central column of the frequency-domain image, define the horizontal range of the filter as the column range from ccol+masklengtha to ccol+masklengthb; on the left side of the central column of the frequency-domain image, define the horizontal range of the filter as the column range from ccol-masklengthb to ccol-masklengtha in the same way. Set the values within the above range area in the mask mask to 0, so as to design the required filter mask mask (as Figure 3 shown).
[0057] 4.4. Apply the designed filter mask mask to the centered frequency-domain image fshift. Specifically, it is implemented by multiplying fshift and mask element by element to obtain the filtered frequency-domain image fshiftwithMask (as Figure 4 shown). By multiplying element by element, apply the mask to the frequency-domain image to filter out specific frequency components of the wood board surface texture and retain the wood board surface defect components.
[0058] The protection scope of the present invention includes but is not limited to the above embodiments. The protection scope of the present invention is subject to the claims. Any substitutions, deformations, and improvements that are easily conceivable by those skilled in the art to this technology fall within the protection scope of the present invention.
Claims
1. An image enhancement method for wood board surface defect detection task, characterized in that: include: Step 1, receive the input grayscale image img_gray of the wooden board surface, and obtain the number of rows and columns of the image; Step 2, analyze the texture features of the grayscale image of the wooden board surface: randomly select several rows in the image, perform fast Fourier transform on each row of data, calculate the normalized single-sided spectrum of the frequency domain signal, and find the first maximum point; record the position of the first maximum point corresponding to each row, calculate the average value of the positions of all the first maximum points, and round down to get the key parameter avg_floor; Step 3, perform a two-dimensional fast Fourier transform on the grayscale image of the wooden board surface to obtain a frequency domain image; perform centralization on the frequency domain image to obtain fshift; Step 4: According to the avg_floor parameter obtained in step 2, a filter mask is designed to weaken the texture of the wooden board; The mask is set to 0 in a specific range in the frequency domain and to 1 in other parts; the designed mask is multiplied by fshift to obtain the filtered frequency domain image fshiftwithMask; Step 5, perform inverse centralization on the filtered frequency domain image fshiftwithMask to obtain fishift; perform two-dimensional inverse fast Fourier transform on fishift to obtain the enhanced image img_back; Step 6. Return the enhanced image img_back as the input for the wood board surface defect detection task.
2. The image enhancement method for wood board surface defect detection task according to claim 1 is characterized in that: The step 2 is specifically as follows: 2.
1. Randomly select the row index of the grayscale image img_gray matrix of the wooden board surface. The row index is less than the number of rows and greater than 0. Get all the grayscale values of the row where the row index is located and save it as the number series y. 2.
2. Perform fast Fourier transform on each row of data y, convert the time domain signal into a frequency domain signal, and obtain the frequency domain signal fft_y corresponding to each row; 2.
3. Calculate the normalized single-sided spectrum of the frequency domain signal, specifically: Calculate the absolute value of the frequency domain signal fft_y to get the double-sided spectrum; then divide the spectrum value by the total number of columns cols for normalization; since the FFT result is symmetrical, only half of the spectrum needs to be analyzed, and the spectrum value of the first half can be taken to get the normalized single-sided spectrum normalizationhalf_y; 2.
4. Find the maximum point in the normalized single-sided spectrum normalizationhalf_y and record the position of the first maximum point, that is, save the index value argrelmax_index of the normalizationhalf_y spectrum series corresponding to the first maximum point; 2.
5. Record the position of the first maximum point argrelmax_index corresponding to the row where the randomly selected row index is located, calculate the average value of all argrelmax_index, and round it down to get the key parameter avg_floor.
3. The image enhancement method for wood board surface defect detection task according to claim 1 is characterized in that: The step 4 is specifically as follows: 4.
1. Create a mask with the same size as the input image, with all elements initialized to 1, that is, create a two-dimensional array matrix mask with all elements set to 1, rows and columns set to cols; 4.
2. Set relevant parameters: Since the frequency domain image is centered in step 3, the center of the spectrum is moved to the center of the image. Therefore, half of the number of rows is taken as crow and half of the number of columns is taken as ccol. crow and ccol represent the index of the center row and center column of the frequency domain image respectively. The width of the filter area is maskwidth. Masklengtha is set to the avg_floor parameter obtained in step 2. Masklengthb is a fixed value. 4.
3. Near the center row of the frequency domain image, the row range from crow-maskwidth to crow+maskwidth defines the vertical range of the filter; on the right side of the center column of the frequency domain image, the column range from ccol+masklengtha to ccol+masklengthb defines the horizontal range of the filter; on the left side of the center column of the frequency domain image, the column range from ccol-masklengthb to ccol-masklengtha also defines the horizontal range of the filter; set the values in the mask mask within the above range to 0, thereby designing the required filter mask mask; 4.
4. Apply the filter mask mask designed in step 4.3 to the centered frequency domain image fshift. Specifically, fshift is multiplied element by element with the filter mask mask constructed in step 4.3 to obtain the filtered frequency domain image fshiftwithMask.
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