A low-illumination image enhancement method based on an improved Retinex algorithm

By converting the low-frequency components of an image from the RGB spatial domain to the HSV spatial domain, performing Gamma brightness correction only on the V channel, and fusing it with the low-frequency components of the image processed by the improved Retinex algorithm, image enhancement is performed using the improved Retinex algorithm. This solves the problem of color and detail fidelity in low-light image processing, improves the real-time performance of image processing and the control capabilities of the production line, and promotes the implementation of smart manufacturing projects.

CN115358948BActive Publication Date: 2026-04-14GUANGXI UNIVERSITY OF TECHNOLOGY
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
GUANGXI UNIVERSITY OF TECHNOLOGY
Filing Date
2022-08-23
Publication Date
2026-04-14

AI Technical Summary

Technical Problem

Existing technologies struggle to simultaneously guarantee color restoration and detail fidelity when enhancing images under low-light conditions, and their processing speed is slow with poor real-time performance.

Method used

The low-frequency components of the image are converted from the RGB spatial domain to the HSV spatial domain. Gamma brightness correction is performed only on the V channel, and then fused with the low-frequency components of the image processed by the improved Retinex algorithm. The improved Retinex algorithm is used to calculate a new center wrap function by weighting a bilateral filter and a Gaussian filter, and then the image is enhanced.

Benefits of technology

It achieves the goal of enhancing image brightness while maintaining image color and smoothness, avoiding local distortion, improving the real-time performance and accurate recognition capabilities of image processing, and is suitable for the application of visual inspection devices in complex lighting environments. It enhances the precision control and process improvement of production lines and promotes the implementation of smart manufacturing projects.

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Abstract

The application discloses a low-illumination image enhancement method based on an improved Retinex algorithm, and applies to the technical field of image enhancement, and comprises the following steps: performing discrete wavelet decomposition on a low-illumination image to obtain low-frequency and high-frequency components of the image; converting the low-frequency component into HSV, separately performing brightness correction on a V channel, then converting back to RGB, performing bilateral filtering, and then converting to HSV to extract the V channel; performing image enhancement on the low-frequency component by using an improved Retinex algorithm based on a joint weighting of a bilateral filter and a Gaussian filter as a new center-surround function, and performing median filtering processing, then converting to HSV to extract the V channel; weighting and fusing the two V channels, retaining the H and S channels after algorithm enhancement, then converting back to RGB, performing discrete wavelet fusion with the high-frequency component after denoising, and stretching and outputting the enhanced low-illumination image. The application can effectively guarantee the color, edge details and avoid local distortion of the image.
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Description

Technical Field

[0001] This invention relates to the field of image enhancement technology, and in particular to a low-light image enhancement method based on an improved Retinex algorithm. Background Technology

[0002] With the development of my country's industrial technology and the rise of its dominant industrial position, the industrial production structure is shifting towards technology- and knowledge-intensive models. Simultaneously, industrial intelligence is rapidly developing, and machine vision is being applied to various production fields, gaining increasing attention as a modern digital measurement method. However, because vision is highly sensitive to illumination, image quality is poor in low-light environments, making it impossible to perceive data about the detected object. Therefore, how to enhance low-light images has become a hot topic in the field of image processing.

[0003] CN113850744A discloses an image enhancement algorithm based on adaptive Retinex and wavelet fusion. Both algorithms are performed in the RGB space. Since the color correlation of images in the RGB domain is high, it is impossible to simultaneously guarantee the color restoration and image details of the enhanced image after image enhancement.

[0004] CN113344798A discloses a dark image enhancement method based on Retinex. The network convolution kernel used is single. Due to its inherent limitations, the extracted features are also limited, which makes it slightly inferior in terms of applicability. This results in local distortion of the processed image and unsatisfactory processing effect.

[0005] CN114418889A discloses a low-light image enhancement method based on a multi-scale network structure. It uses a multi-scale network structure image enhancement model to enhance the image, while restoring the color distortion of the image. However, it requires a relatively complex calculation process and has high hardware requirements. In addition, its processing speed is slower than that of general image enhancement algorithms, and its real-time performance is poor.

[0006] Therefore, how to provide a low-light image enhancement method based on the improved Retinex algorithm that can effectively preserve the color and edge details of the image and avoid local distortion is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0007] In view of this, the present invention proposes a low-light image enhancement method based on an improved Retinex algorithm. By converting the low-frequency components of an image from the RGB spatial domain to the HSV spatial domain, and performing Gamma correction only on the V channel, and then fusing it with the low-frequency components processed by the improved Retinex algorithm, the image is converted back to the RGB spatial domain. By performing Gamma correction on the V channel and fusing the low-frequency components in the HSV spatial domain, the image brightness is corrected while effectively preserving the image color, avoiding local distortion. The improved Retinex algorithm, which involves weighting a bilateral filter and a Gaussian filter to obtain a new center-around function for image enhancement, achieves image enhancement while maintaining image smoothness and improving contrast. The improved algorithm also protects image edge details, avoiding distortion of some image details. Furthermore, image enhancement of low-light images using the improved Retinex algorithm is beneficial for the application of visual inspection devices in complex lighting environments, improving the versatility of the inspection device and enabling accurate identification of inspection targets. This not only allows for precise control of the production line but also enables significant improvements in process technology, enhancing overall production efficiency and promoting the construction and implementation of specific enterprise projects (smart manufacturing).

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A low-light image enhancement method based on an improved Retinex algorithm includes:

[0010] Step (1): Obtain the low-light image and perform discrete wavelet decomposition to obtain the low-frequency component and high-frequency component of the first image.

[0011] Step (2): Convert the low-frequency component of the first image from the RGB spatial domain to the HSV spatial domain, and perform brightness correction on the V channel separately to obtain the low-frequency component of the second image. Then, convert the low-frequency component of the second image back to the RGB spatial domain for bilateral filtering and then back to the HSV spatial domain to obtain the low-frequency component of the third image, and extract the V channel of the low-frequency component of the third image.

[0012] Step (3): The improved Retinex algorithm based on the joint weighting of bilateral filter and Gaussian filter as the new center wrap function is used to enhance the low frequency component of the first image and perform median filtering to obtain the low frequency component of the fourth image. Then, the low frequency component of the fourth image is converted from the RGB space domain to the HSV space domain to obtain the low frequency component of the fifth image, and the V channel of the low frequency component of the fifth image is extracted.

[0013] Step (4): The V channel of the low-frequency component of the third image is weighted and fused with the V channel of the low-frequency component of the fifth image, and the H and S channels of the low-frequency component of the fifth image are retained to obtain the low-frequency component of the sixth image. Then, the low-frequency component of the sixth image is converted from the HSV space domain to the RGB space domain to obtain the low-frequency component of the seventh image.

[0014] Step (5): Denoise the high-frequency components of the first image to obtain the high-frequency components of the second image. Then, perform discrete wavelet fusion on the low-frequency components of the seventh image and the high-frequency components of the second image, and stretch the image to output the enhanced low-light image.

[0015] Optionally, in step (1), the expression for discrete wavelet decomposition is as follows:

[0016]

[0017]

[0018] in, The low-frequency component of the first image; The first image high-frequency components include: horizontal high-frequency component H, vertical high-frequency component V, and diagonal high-frequency component D; It is a two-dimensional scaling function for discrete wavelets; Y(i,j) is a two-dimensional scaling function in the horizontal, vertical, and diagonal directions; MN is the low-light image; l0 is the initial function scale; and m and n are discrete offsets.

[0019] Optionally, in step (2), the expression for converting the low-frequency components of the first image from the RGB spatial domain to the HSV spatial domain is as follows:

[0020]

[0021]

[0022] V = max

[0023] Where r, g, and b are the red, green, and blue channels of the image, respectively, ranging from 0 to 1; max is the maximum value in RGB, and min is the minimum value in RGB.

[0024] Optionally, in step (2), the brightness of the V channel is corrected separately using Gamma, with a Gamma value of 0.5.

[0025] Optionally, in step (3), the expression for the improved Retinex algorithm is as follows:

[0026]

[0027] Where N is the number of Gaussian wrapping functions; w n * represents the weighting coefficients; * represents the convolution operator; n represents the n different scales of the Gaussian wrap function; R(i,j) represents the reflection component; I(i,j) represents the original image (the low-frequency component of the first image); h n (i,j) is the new center-encircling function obtained by weighting the bilateral filter and the Gaussian filter together.

[0028] Optionally, in step (3), median filtering is performed by: excluding the pixel value at the center of the window, sorting the remaining pixel values, and replacing the original pixel value at the center of the window with the median data to obtain the filtered data.

[0029] Optionally, in step (4), the expression for the low-frequency component of the seventh image is as follows:

[0030] C = V × S

[0031] X = C × (1 - |(H / 60°) mod 2 - 1|)

[0032] m=VC

[0033]

[0034] (R,G,B)=((R'+m)×255,(G'+m)×255,(B'+m)×255)

[0035] Where: H is hue, with a value range of 0-360 degrees; S is saturation, with a value range of 0-1; V is saturation, with a value range of 0-1.

[0036] Optionally, in step (5), the expression for discrete wavelet fusion is as follows:

[0037]

[0038]

[0039] in, The low-frequency component of the first image; The first image high-frequency components include: horizontal high-frequency component H, vertical high-frequency component V, and diagonal high-frequency component D; It is a two-dimensional scaling function for discrete wavelets; Z(i,j) is a two-dimensional scaling function in the horizontal, vertical, and diagonal directions; Z(i,j) is the fused and enhanced low-light image; MN is the pixel size of the image; l0 is the initial function scale; m and n are discrete offsets.

[0040] As can be seen from the above technical solutions, compared with the prior art, the present invention proposes a low-light image enhancement method based on the improved Retinex algorithm. By converting the low-frequency components of an image from the RGB spatial domain to the HSV spatial domain, and performing Gamma correction only on the V channel, and then fusing it with the low-frequency components processed by the improved Retinex algorithm, the image is converted back to the RGB spatial domain. By performing Gamma correction on the V channel and fusing the low-frequency components in the HSV spatial domain, the image brightness is corrected while effectively preserving the image color, avoiding local distortion. The improved Retinex algorithm, which involves weighting a bilateral filter and a Gaussian filter to obtain a new center-around function for image enhancement, achieves image enhancement while maintaining image smoothness and improving contrast. The improved algorithm also protects image edge details, avoiding distortion of some image details. Furthermore, image enhancement of low-light images using the improved Retinex algorithm is beneficial for the application of visual inspection devices in complex lighting environments, improving the versatility of the inspection device and enabling accurate identification of inspection targets. This not only allows for precise control of the production line but also enables significant improvements in process technology, enhancing overall production efficiency and promoting the construction and implementation of specific enterprise projects (smart manufacturing). Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0042] Figure 1 This is a schematic diagram of the process of the present invention.

[0043] Figure 2 This is a schematic diagram of the median filtering method of the present invention. Detailed Implementation

[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] Embodiment 1 of this invention discloses a low-light image enhancement method based on an improved Retinex algorithm, such as... Figure 1 As shown, it includes:

[0046] Step (1): Obtain the low-light image and perform discrete wavelet decomposition using Matlab to obtain the low-frequency component and high-frequency component of the first image, as shown in the following expressions:

[0047]

[0048]

[0049] in, The low-frequency component of the first image; The first image high-frequency components include: horizontal high-frequency component H, vertical high-frequency component V, and diagonal high-frequency component D; It is a two-dimensional scaling function for discrete wavelets; Y(i,j) is a two-dimensional scaling function in the horizontal, vertical, and diagonal directions; Y(i,j) is the original image (low-light image); MN is the pixel size of the image; l0 is the initial function scale; m and n are discrete offsets.

[0050] Step (2): When performing calculations in the RGB spatial domain, due to the high correlation between the three RGB channels, the processed image may exhibit over-enhancement and local distortion. Therefore, the low-frequency components of the first image are converted from the RGB spatial domain to the HSV spatial domain. In the HSV domain, the correlation between the channels is low, and the above problems will not occur as a result of processing in the RGB spatial domain. The expression is as follows:

[0051]

[0052]

[0053] V = max

[0054] Where r, g, and b are the red, green, and blue channels of the image, respectively, and are real numbers between 0 and 1; max is the maximum value in RGB, and min is the minimum value in RGB.

[0055] The brightness of the V channel is corrected separately using Gamma, with a Gamma value of 0.5, to obtain the low-frequency component of the second image. Then, the low-frequency component of the second image is converted back to the RGB spatial domain for bilateral filtering (noise points will appear in the image after brightness correction, so bilateral filtering is required for the processed image) and then converted back to the HSV spatial domain to obtain the low-frequency component of the third image. The V channel of the low-frequency component of the third image is extracted for the next step of image low-frequency component fusion.

[0056] Step (3): An improved Retinex algorithm based on a weighted sum of bilateral and Gaussian filters as a new center wrap function is used to enhance the low-frequency components of the first image. Compared with the traditional Retinex algorithm, it has further improvements in image smoothness preservation, contrast enhancement, and edge preservation. The process of deriving the improved Retinex algorithm is as follows:

[0057] Algorithms based on Retinex theory include the SSR algorithm, MSR algorithm, and MSRCR algorithm; the central wrapping function of the single-scale Retinex algorithm is a Gaussian function, which can be expressed as:

[0058] I(i,j)=R(i,j)L(i,j)

[0059] Where I(i,j) is the original image (low-frequency component of the first image); R(i,j) is the reflection component; and L(i,j) is the incident component.

[0060] By performing a logarithmic transformation, we obtain:

[0061] Log[R(i,j)]=Log[I(i,j)]-Log[I(i,j)*f(i,j)]

[0062] Where * represents the convolution operator; f(i,j) is the Gaussian wrapping function, expressed as follows:

[0063]

[0064] Where c is the Gaussian normalization condition, σ is the Gaussian wrap-around scale, and the following conditions are satisfied:

[0065] ∫∫f(i,j)didj=1

[0066] The Gaussian kernel parameter in single-scale Retinex directly affects the image processing result, and its singular parameter leads to the strong limitations of SSR. To improve the limitations of the SSR algorithm, the multi-scale Retinex algorithm combines local and global image information and performs weighted calculations using Gaussian wrapping functions at different scales, as shown in the following expression:

[0067]

[0068] Where N is the number of Gaussian wrapping functions; w n For weights; * represents the convolution operator; n represents the n different scales of the Gaussian wrap function, f n (i,j) is the Gaussian wrapping function at the nth scale;

[0069] While traditional MSR avoids the single-scale problem, its center-around function is still a Gaussian filter, which increases image noise, causing distortion of some image details and resulting in poor image enhancement quality. Therefore, this paper improves upon MSR by weightedly fusing a bilateral filter with a Gaussian filter to form a new center-around kernel function for image enhancement.

[0070] The expression for the bilateral filter is as follows:

[0071]

[0072] Where w(i,j,k,l) ​​are the bilateral weighting coefficients, which are the product of the spatial domain kernel d(i,j,k,l) ​​and the value domain kernel r(i,j,k,l), and can be expressed as:

[0073]

[0074] Where f(x,y) is the pixel value of the image at point (x,y); f(k,l) is the pixel value of the image at point (k,l); σ d σ is the standard deviation kernel function of the Gaussian function; r (k,l) represents the standard deviation of the Gaussian function; (k,l) represents the coordinates of the center point of the template window; and (x,y) represents the coordinates of a defined point.

[0075] f n (i,j)g(i,j) is combined with weighted fusion to obtain a new central wrapping function h. n Given (i,j), the improved Retinex algorithm is expressed as follows:

[0076]

[0077] Among them, h n (i,j) is the new center-encircling function obtained by weighting the bilateral filter and the Gaussian filter together.

[0078] Median filtering is then performed to obtain the low-frequency components of the fourth image. The median filtering is as follows: Figure 2 As shown, the process involves excluding the pixel value of the center point of a 3x3 neighborhood window, sorting the remaining pixel values, and replacing the original pixel value of the center point with the median data to obtain the filtered data.

[0079] The low-frequency component of the fourth image is then converted from the RGB spatial domain to the HSV spatial domain to obtain the low-frequency component of the fifth image. The V channel of the low-frequency component of the fifth image is then extracted to facilitate the next step of image low-frequency component fusion.

[0080] Step (4): The V channel of the low-frequency component of the third image is weighted and fused with the V channel of the low-frequency component of the fifth image, and the H and S channels of the low-frequency component of the fifth image are retained to obtain the low-frequency component of the sixth image. Then, the low-frequency component of the sixth image is converted from the HSV spatial domain to the RGB spatial domain to obtain the low-frequency component of the seventh image. The expression of the low-frequency component of the seventh image is as follows:

[0081] C = V × S

[0082] X = C × (1 - |(H / 60°) mod 2 - 1|)

[0083] m=VC

[0084]

[0085] (R,G,B)=((R'+m)×255,(G'+m)×255,(B'+m)×255)

[0086] Where: H is hue, with a value range of 0-360 degrees; S is saturation, with a value range of 0-1; V is saturation, with a value range of 0-1.

[0087] Step (5): Denoise the high-frequency components of the first image to obtain the high-frequency components of the second image. The high-frequency components of the first image obtained by discrete wavelet transform decomposition are the edge contours and image details of the original image. In most cases, the noise in the image is also high-frequency, so it is necessary to improve the image quality through image denoising. While removing noise, we also need to preserve the effective edge details of the image. Then, the low-frequency components of the seventh image and the high-frequency components of the second image are fused by discrete wavelet. The expression for discrete wavelet fusion is as follows:

[0088]

[0089]

[0090] in, The low-frequency component of the first image; The first image high-frequency components include: horizontal high-frequency component H, vertical high-frequency component V, and diagonal high-frequency component D; It is a two-dimensional scaling function for discrete wavelets; Z(i,j) is a two-dimensional scaling function in the horizontal, vertical, and diagonal directions; Z(i,j) is the reconstructed image (the fused and enhanced low-light image); MN is the pixel size of the image; l0 is the initial function scale; m and n are discrete offsets.

[0091] It also performs image stretching to improve image contrast and outputs an enhanced low-light image.

[0092] This invention discloses a low-light image enhancement method based on an improved Retinex algorithm. By converting the low-frequency components of an image from the RGB spatial domain to the HSV spatial domain, and performing Gamma correction only on the V channel, and then fusing it with the low-frequency components processed by the improved Retinex algorithm, the image is converted back to the RGB spatial domain. By performing Gamma correction on the V channel and fusing the low-frequency components in the HSV spatial domain, the image brightness is corrected while effectively preserving the image color, avoiding local distortion. The improved Retinex algorithm, which involves weighting a bilateral filter and a Gaussian filter to obtain a new center-around function for image enhancement, achieves image enhancement while maintaining image smoothness and improving contrast. The improved algorithm also protects image edge details, avoiding distortion of some image details. Furthermore, image enhancement of low-light images using the improved Retinex algorithm is beneficial for the application of visual inspection devices in complex lighting environments, improving the versatility of the inspection device and enabling accurate identification of inspection targets. This not only allows for precise control of the production line but also enables significant improvements in process technology, enhancing overall production efficiency and promoting the construction and implementation of specific enterprise projects (smart manufacturing).

[0093] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0094] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A low-illumination image enhancement method based on an improved Retinex algorithm, characterized in that, include: Step (1): Acquire a low-light image and perform discrete wavelet decomposition to obtain the low-frequency component and high-frequency component of the first image; Step (2): Convert the first image low-frequency component from the RGB spatial domain to the HSV spatial domain, and perform brightness correction on the V channel separately to obtain the second image low-frequency component. Then, convert the second image low-frequency component back to the RGB spatial domain for bilateral filtering and then back to the HSV spatial domain to obtain the third image low-frequency component, and extract the V channel of the third image low-frequency component. Step (3): The improved Retinex algorithm based on the joint weighting of bilateral filter and Gaussian filter as the new center wrap function is used to enhance the low frequency component of the first image and perform median filtering to obtain the low frequency component of the fourth image. Then, the low frequency component of the fourth image is converted from the RGB space domain to the HSV space domain to obtain the low frequency component of the fifth image, and the V channel of the low frequency component of the fifth image is extracted. Step (4): The V channel of the third low-frequency component of the image and the V channel of the fifth low-frequency component of the image are weighted and fused, and the H and S channels of the fifth low-frequency component of the image are retained to obtain the sixth low-frequency component of the image. Then, the sixth low-frequency component of the image is converted from the HSV space domain to the RGB space domain to obtain the seventh low-frequency component of the image. Step (5): Denoise the high-frequency component of the first image to obtain the high-frequency component of the second image. Then, perform discrete wavelet fusion on the low-frequency component of the seventh image and the high-frequency component of the second image, and stretch the image to output the enhanced low-light image. In step (3), the expression for the improved Retinex algorithm is as follows: where N is the number of Gaussian surround functions; w n is a weight coefficient; * is a convolution operator symbol; n is n different scales of Gaussian surround functions; R(i,j) is a reflection component; I(i,j) is a low-frequency component of the first image; h n (i,j) is a new center surround function obtained by combining the bilateral filter and the Gaussian filter with weighting.

2. The low-illumination image enhancement method based on the improved Retinex algorithm according to claim 1, characterized in that, In step (1), the expression for the discrete wavelet decomposition is as follows: wherein, is the low frequency component of the first image; is the high frequency component of the first image, including: horizontal high frequency component H, vertical high frequency component V, diagonal high frequency component D; is the two-dimensional scaling function of discrete wavelet; is the two-dimensional scaling function in horizontal, vertical and diagonal directions; Y(i,j) is the low-illumination image; MN is the pixel size of the image; l0 is the initial function scale; m, n are the discrete offsets.

3. The low-illumination image enhancement method based on the improved Retinex algorithm according to claim 1, characterized in that, In step (2), the expression for converting the low-frequency components of the first image from the RGB spatial domain to the HSV spatial domain is as follows: V = max Where r, g, and b are the red, green, and blue channels of the image, respectively, ranging from 0 to 1; max is the maximum value in RGB, and min is the minimum value in RGB.

4. The low-illumination image enhancement method based on the improved Retinex algorithm according to claim 1, characterized in that, In step (2), Gamma is used to correct the brightness of the V channel separately, and the Gamma value is 0.

5.

5. The low-illumination image enhancement method based on the improved Retinex algorithm according to claim 1, characterized in that, In step (3), the median filtering is as follows: the pixel value of the center point of the window is excluded, the remaining pixel values ​​are sorted, and the median data is used to replace the original pixel value of the center point of the window to obtain the filtered data.

6. The low-light image enhancement method based on the improved Retinex algorithm according to claim 1, characterized in that, In step (4), the expression for the low-frequency component of the seventh image is as follows: C = V × S X = C × (1 - |(H / 60°) mod 2 - 1|) m=VC (R,G,B)=((R'+m)×255,(G'+m)×255,(B'+m)×255) Where: H is hue, with a value range of 0-360 degrees; S is saturation, with a value range of 0-1; V is saturation, with a value range of 0-1.

7. A low-light image enhancement method based on an improved Retinex algorithm according to claim 1, characterized in that, In step (5), the expression for the discrete wavelet fusion is as follows: in, The low-frequency component of the first image; The high-frequency components of the first image include: horizontal high-frequency component H, vertical high-frequency component V, and diagonal high-frequency component D; It is a two-dimensional scaling function for discrete wavelets; Z(i,j) is a two-dimensional scaling function in the horizontal, vertical, and diagonal directions; Z(i,j) is the fused and enhanced low-light image; MN is the pixel size of the image; l0 is the initial function scale; m and n are discrete offsets.

Citation Information

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