A low-light image enhancement method based on adaptive illumination initialization

Abstract

The present invention relates to a low-light image enhancement method based on adaptive illumination initialization, and relates to technical fields such as digital image processing, computer vision, signal processing, and image enhancement. The specific steps are as follows: 1) Collect and organize existing publicly available low-light image datasets on the Internet; 2) Based on the proposed illumination adaptive initialization module, accurately estimate the initial illumination component of the image according to different input images; 3) Under the constraint of the structured illumination prior, optimize and estimate the initial illumination component through the alternating direction minimization technique; 4) Perform gamma correction on the obtained optimized illumination component to further achieve non-linear adjustment of the image brightness; 5) Combine the Retinex theory model to achieve the enhancement of low-light images. This method uses the accurately estimated initial illumination component and combines the Retinex theory model to achieve the enhancement task of low-light images, and can also be used for the enhancement of low-light videos. The invention has practical application significance and achieves satisfactory enhancement effects at the same time.

Description

Technical Field

[0001] The present invention relates to a low-light image enhancement method based on adaptive illumination initialization, and belongs to the technical fields of computer vision, digital image processing, signal processing, image enhancement, etc. Background Art

[0002] As an important carrier tool for modern information resource exchange and transmission, digital images play an increasingly important role in today's society. It can be said that people have come into contact with relevant computer vision, either consciously or unconsciously, in their daily activities such as clothing, food, housing, and transportation. For example, fingerprint locks used when going out, face recognition used when entering office buildings, and the camera functions of smartphones, etc., all involve it. And it also plays a crucial role in many fields such as medical imaging diagnosis, satellite remote sensing, military reconnaissance, underwater image shooting, and electronic video surveillance. Thus, it can be seen that computer vision and digital images occupy an absolutely important position in our human life. In recent years, people's material living standards have been comprehensively improved, and photographic electronic devices such as digital single-lens reflex cameras and smart phones have gradually entered the public's field of vision and have been widely used. As a result, people can more easily and conveniently shoot, share, and transmit images. While greatly enriching people's lifestyles, it has also brought digital images to an unprecedented exponential growth era, making computer vision face various severe tests and challenges. Facing such a huge amount of digital images, many of them have a low overall brightness due to the relatively dark imaging environment or insufficient performance of hardware devices (aperture size, exposure time), and a lot of content information in the images is submerged in the darkness. And this kind of low-light image with poor visual quality not only affects people's subjective visual observation, but also has varying degrees of influence on subsequent computer vision tasks, including image segmentation, image classification, and object detection, etc.

[0003] As a classic task in computer vision, image enhancement includes many directions such as image restoration, image deblurring, and low-light image enhancement, and has always been a popular topic in the visual field. As one of the most important branches in the field of image enhancement, low-light image enhancement has also been deeply analyzed and discussed by a large number of researchers in recent years. Briefly summarized, the core of the low-light image enhancement task is to improve the brightness information of the image, so that the content hidden in the darkness can be revealed, and the structural information and texture details of the image are enhanced, aiming to improve the visual quality of the image and also facilitate the subsequent related image processing operations.

[0004] To solve the above problems existing in low-light images, many excellent enhancement methods have been proposed in the past few decades. Here we roughly divide these methods into those based on traditional theoretical models and those based on deep learning. For traditional low-light image enhancement methods, they can be specifically divided into algorithms based on histogram equalization, algorithms based on image dehazing, algorithms based on image fusion, and algorithms based on the Retinex theoretical model. However, considering that image decomposition estimation is a highly singular problem, for low-light image enhancement based on the Retinex model, how to accurately estimate the illumination component of the image has always been a key problem to be solved. Most previous methods have constrained the optimal estimation of the illumination component through various assumptions and prior knowledge, but rarely considered the initialization problem of the image illumination component. However, the initial illumination component not only directly determines the accuracy of subsequent optimal estimation operations, but also is related to the quality of the final enhancement result.

[0005] CN111292257A, an image enhancement method based on Retinex in a dark visual environment, the method includes: obtaining image data and dividing the image data into a global illumination map and a local illumination map; performing weighted averaging on the corresponding pixel points of the two images to obtain a preliminary estimated illumination map, using an improved weighted guided filter to perform edge-preserving smoothing filtering on the preliminary estimated illumination map, and performing improved adaptive Gamma correction on the filtered illumination map to obtain a corrected estimated illumination map; using the Retinex algorithm to calculate the reflection maps of the R channel, G channel, and B channel using the original image and the corrected estimated illumination map, and synthesizing the reflection maps of the three channels to obtain an enhanced image; the present invention can enhance the image in a dark visual environment while retaining the details of the bright area and reducing the halo effect, avoiding over-enhancement of the image, and facilitating processing such as recognition and detection of images in a dark visual environment.

[0006] Although this patent proposes a local illumination map, in fact, it only performs per-pixel weighted averaging on the two illumination components, without considering the content correlation between the pixels of the local blocks of the image, resulting in overexposure / underexposure in the enhancement result. In the present invention, we traverse each channel of the input image through a designed 3×3 local block, truly realizing the correlation perception of the content of adjacent pixels of the image, thereby more accurately initializing the illumination component, and finally adaptively realizing the image enhancement task for the exposure levels of different regions of the image. Summary of the Invention

[0007] The present invention aims to solve the above problems of the prior art. A low-light image enhancement method based on adaptive illumination initialization is proposed. The technical solution of the present invention is as follows:

[0008] A low-light image enhancement method based on adaptive illumination initialization, which includes the following steps:

[0009] (1) Collect and organize the existing publicly available low-light image datasets on the Internet;

[0010] (2) Based on the proposed illumination adaptive initialization module according to different input images, (the illumination adaptive initialization module means that by traversing the image pixel by pixel and taking the maximum value in the local 3×3 block, the relevance of the local content information of the image is considered, and the illumination weight matrix of the input image is adaptively obtained to accurately estimate the initial illumination component of the image;

[0011] (3) Under the constraint of the structured illumination prior, optimize and estimate the initial illumination component by the alternating direction method of multipliers;

[0012] (4) Perform gamma correction on the obtained optimized illumination component to non-linearly adjust the brightness of the image;

[0013] (5) Combine the Retinex theory model to enhance the low-light image.

[0014] Furthermore, step (2) estimates the initial illumination component of the image based on the proposed illumination adaptive initialization module according to different input images, specifically including:

[0015] The typical image illumination initialization operations in step (2) include taking the maximum value of the R, G, and B channels, taking the average value of the R, G, and B channels, and taking the V component in the HSV space,

[0016] The H component represents hue, the S component represents saturation, and the V component represents brightness

[0017] The specific formula is as follows:

[0018]

[0019] where, I 0 (x) is the initial illumination component, c includes the three color channels of R, G, and B, and S c (x) is the maximum value component in the three color channels, is the illumination weight matrix, Ω represents the local block centered on x, and the block size is taken as 3×3 in this article, is the illumination adjustment parameter.

[0020] Furthermore, step (3) optimizes and estimates the initial illumination component by the alternating direction method of multipliers under the constraint of the structured illumination prior, specifically including:

[0021] The objective function of the ideal image illumination component optimization algorithm is as follows:

[0022]

[0023] Among them, I 0 represents the initial illumination component, I represents the optimized illumination component, W is the structural weight matrix, is the first-order derivative filter, which is specifically divided into the horizontal direction and the vertical direction in two parts, ||·|| 1 and ||·|| F are the 1-norm and the standard F-norm respectively. In the above objective function, the first term is the data fidelity term, which is used to constrain the difference between I 0 and I. The role of the regularization term is to limit the size of the solution space. The coefficient α is used to balance the fidelity term and the regularization term to achieve the structural-aware smoothing of the illumination component;

[0024] The weight matrix W is designed to perceive the structural edge information of the image, and specifically includes the following horizontal direction W h (x) and the vertical direction W v (x) in two parts, specifically:

[0025]

[0026] Among them, G σ (x, y) represents the Gaussian kernel function with a standard deviation of σ, and there is dist(x, y) represents the spatial Euclidean distance between pixels x and y. ε is a very small constant to avoid the denominator being zero, and |·| represents the absolute value operation.

[0027] Perform an approximate simplification operation on the above objective function. First, expand the regularization term in the objective function to get

[0028]

[0029] W d (x) is the structural weight matrix, and d among them includes the horizontal direction h and the vertical direction v.

[0030] Here, use to approximately replace the regularization term Finally, the above formula can be equivalently written in the following form,

[0031]

[0032] Specifically, when the value is very small, the value is also relatively small, and the value of

[0033] Further, in step (4), gamma correction is performed on the obtained optimized illumination component to perform non-linear adjustment on the brightness of the image. The specific formula is as follows:

[0034] I g (x) = I(x) γ

[0035] where γ takes a value of 0.8, and the final enhancement result S is obtained by combining the input image S(x) and the optimized illumination component I g after illumination adjustment, in combination with the Retinex model out ;

[0036]

[0037] Here, ε is a very small constant to avoid the denominator being zero.

[0038] Further, the core idea of the Retinex theory model is to decompose the observed image into two parts: an illumination component and a reflection component. The illumination component represents the distribution of illumination in the image scene and contains the structural information of the image; while the reflection component represents the inherent properties of the object, mainly represented by the texture details and color information of the image. The specific formula is as follows:

[0039]

[0040] where S(x) represents the input original low-light image, I(x) represents the illumination component, R(x) is the reflection component, x represents a specific pixel, and the operator represents an element-wise multiplication operation.

[0041] The advantages and beneficial effects of the present invention are as follows:

[0042] The present invention utilizes technologies such as computer vision, digital image processing, signal processing, and image enhancement to achieve the task of low-light image enhancement. Based on the Retinex theory model, the present invention proposes a simple and effective method for adaptively initializing the illumination component, accurately estimating the illumination component of the image, and thus achieving a satisfactory low-light image enhancement effect. The present invention has the following advantages:

[0043] (1) Training and testing related experiments are carried out based on the matlab software platform, with low costs;

[0044] (2) It is a low-light image enhancement method based on the Retinex theory model, which proposes a simple and effective adaptive illumination initialization module and has better enhancement results than existing methods;

[0045] (3) The low-light image enhancement method proposed by the present invention has good enhancement effects on low-quality images including low-exposure images, unevenly illuminated images, backlit images, and night images, etc.;

[0046] (4) The present invention also has a certain enhancement effect on videos taken in low-light environments;

[0047] (5) The present invention has a satisfactory enhancement effect. In multiple commonly used low-light image datasets, it shows better enhancement effects and objective evaluation indicators than the existing methods proposed, and at the same time maintains good computational efficiency;

[0048] (6) It helps to improve the performance of downstream advanced vision tasks such as object detection, instance segmentation, and image classification, etc., and can also be used in practical application scenarios such as autonomous driving technology, which has practical significance.

[0049] In the low-light image enhancement method based on the Retinex theory model introduced above, considering that image decomposition estimation is a highly singular problem, how to accurately estimate the illumination component of the image has always been a key difficult problem to be solved by this type of method. And the previous methods based on the Retinex theory model have roughly the same basic operation process, and the main difference in the methods proposed by everyone lies in the problem of how to estimate the illumination component of the image. Most of the previous methods focused on discussing how to more accurately constrain the optimization estimation of the illumination component, but the researchers rarely considered the initialization problem of the image illumination component. However, the initial illumination component of the low-light image not only directly determines the accuracy of the subsequent optimization estimation operation, but also is related to the quality of the final enhancement result. Therefore, this paper proposes a simple and effective method. By considering the relevance of the local content information of the image, the maximum values of the three channels of the color image and the corresponding illumination weight matrix obtained by local block scanning are extracted respectively to accurately estimate the initial illumination component of the image, and then to achieve more effective enhancement of the low-light image. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is the main flowchart of the system of the preferred embodiment provided by the present invention;

[0051] Figure 2 (a1)-(a3) are respectively the initial illumination component obtained by taking the maximum values of the RGB three channels of the input image, its corresponding optimized illumination component, and the enhancement result;

[0052] Figure 2 (b1)-(b3) are respectively the initial illumination component obtained by taking the average values of the RGB three channels of the input image, its corresponding optimized illumination component, and the enhancement result;

[0053] Figure 2(c1)-(c3) are respectively the initial illumination component obtained by taking the brightness V channel of the input image in the HSV color space, its corresponding optimized illumination component, and the enhancement result. Detailed implementation manners

[0054] The following will clearly and detailedly describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. The described embodiments are only a part of the embodiments of the present invention.

[0055] The technical solution for the present invention to solve the above technical problems is:

[0056] Preferably, as Figure 1 shown, a flowchart of a low-light image enhancement method based on adaptive illumination initialization includes the following steps:

[0057] The first step: Collect and organize the existing publicly available low-light image datasets on the Internet for the low-light image enhancement task;

[0058] The second step: Based on the proposed illumination adaptive initialization module, accurately estimate the initial illumination component of the image according to different input images;

[0059] The third step: Under the constraint of the structured illumination prior, optimize and estimate the initial illumination component by the alternating direction minimization technique;

[0060] The fourth step: Perform gamma correction on the obtained optimized illumination component to further perform non-linear adjustment on the brightness of the image;

[0061] The fifth step: Combine the Retinex theory model to achieve the enhancement of low-light images.

[0062] Due to the high uncertainty of the illumination component decomposition estimation, how to accurately estimate the illumination component of the image has always been a difficult problem to be solved by the image enhancement method based on the Retinex model. Most of the previous methods have constrained the optimized estimation of the illumination component through various priors and assumptions, however, the initialization problem of the illumination component has rarely been concerned. The present invention aims at the above problems and proposes an adaptive illumination initialization method to accurately estimate the illumination component of the image and achieve low-light image enhancement. The specific steps are as follows:

[0063] At the beginning, we first give a brief introduction to the Retinex model. Inspired by the human eye retina imaging, Land et al. proposed the Retinex theory model based on color constancy. The core idea of this model is to decompose the observed image into two parts: an illumination component and a reflection component. The illumination component represents the distribution of illumination in the image scene and contains the structural information of the image; while the reflection component represents the inherent properties of the object and is mainly represented by the texture details and color information of the image. Its formula is specifically as follows:

[0064]

[0065] Among them, S(x) represents the input original low-light image, I(x) represents the illumination component, R(x) is the reflection component, x represents a specific pixel, and the operator represents the element-wise multiplication operation. Here, we assume that the illumination components in the three color channels of the color image are the same.

[0066] As the first step of the method based on the Retinex theory model, we outline several commonly used methods in the past, including 1) As the earliest proposed color constancy method, taking the maximum value of the R, G, and B channels of the image as the initial illumination component I 0 (x); 2) Later, some researchers took the average value of the three color channels to initialize the illumination component; 3) Some people also converted the image from the RGB color space to the HSV space and took the brightness channel V as the initial illumination component. The specific formulas are as follows:

[0067]

[0068] I 0 (x) = S V (x)

[0069] Among them, I 0 (x) represents the initial illumination component, c contains different color channels, and S V (x) represents the V component of the image in the HSV color space.

[0070] Most of the previous low-light image enhancement methods based on the Retinex model used the above methods to initialize the illumination component. However, these methods did not consider the local consistency characteristics of the illumination, resulting in the inability to well protect the structural information in the local area of the image. Moreover, the method of taking the average value of the three color channels ignored the range prior of the illumination component, that is, the brightness of the illumination component should not be less than the original image. From the formula of the Retinex theory model, it can be known that the estimation of the illumination component has a direct relationship with the reflection component and also affects the final enhancement result. Therefore, accurately decomposing and estimating the illumination component of the image is crucial for the low-light image enhancement method based on the Retinex model, and the initialization of the illumination component as the first step is particularly critical.

[0071] Based on this, this paper proposes a simple and effective method to achieve accurate initialization of the illumination component. The specific formula is as follows:

[0072]

[0073] Among them, It is the illumination weight matrix. Ω represents the local block centered at x. In this paper, the block size is 3×3. It is the illumination adjustment parameter. By introducing the illumination weight matrix W I , we take into account the local consistency characteristic of illumination, making up for the lack of perception of local illumination content in previous initialization methods. In addition, we also consider the range prior of the illumination component, cleverly restricting the reflection component to [0, 1], avoiding the problems of color distortion of the reflection component and overexposure of the enhancement result.

[0074] After introducing the Retinex theory model and the illumination component adaptive initialization module proposed in this paper, we will next optimize and estimate the initial illumination component through the alternating direction minimization technique under the constraint of the structured light prior. According to the previous analysis, we know that an ideal image illumination component optimization algorithm should take into account both maintaining the overall structure of the image and the smoothness of texture details. Therefore, we have the following objective function:

[0075]

[0076] Among them, I 0 represents the initial illumination component, I represents the optimized illumination component, W is the structure weight matrix, is the first-order derivative filter, which is specifically divided into (horizontal direction) and (vertical direction) two parts, ||·|| 1 and ||·|| F are the 1-norm and the standard F-norm respectively. In the above objective function, the first term is the data fidelity term, used to constrain the difference between I 0 and I. The role of the regularization term is to limit the size of the solution space. The coefficient α is used to balance the fidelity term and the regularization term to achieve the structural perception smoothness of the illumination component.

[0077] The weight matrix W aims to perceive the structural edge information of the image, specifically including the following horizontal direction W h (x) and the vertical direction W v (x) two parts. Specifically, there are:

[0078]

[0079] It can be seen from the above formula that the structure weight matrix W is constructed based on the initial illumination component obtained in the previous text of ours, rather than the optimized illumination component, that is, it shows that the structure weight matrix only needs to be calculated once in this paper, thus effectively shortening the execution time of the algorithm. On the other hand, it also emphasizes the importance of the initial illumination component again.

[0080] To further improve the computational efficiency of the algorithm, we perform an approximate simplification operation on the above objective function. First, we expand the regularization term in the objective function to get

[0081]

[0082] Here we use to approximately replace the regularization term Finally, the above formula can be equivalently written in the following form

[0083]

[0084] Specifically, when is very small, is also relatively small, and will also be suppressed. That is, the finally optimized estimated illumination component I avoids generating gradient changes at positions where the gradient of the initial illumination component is small, and vice versa. This shows that the regularization

[0085] term in the above formula has the same constraint on the structural edges of the illumination component as the original objective function.

[0086] For the task of low-light image enhancement, improving the image brightness is one of the core issues to be solved. Therefore, after obtaining the optimized illumination component, we also need to perform gamma correction on it to achieve non-linear adjustment of the image brightness and further improve the enhancement result. The specific formula is

[0087] I g (x) = I(x) γ

[0088] where γ takes the value of 0.8. We combine the input image S(x) and the optimized illumination component I g after illumination adjustment, and use the Retinex model to obtain the final enhanced result S out .

[0089]

[0090] Here, ε is a very small constant to avoid the denominator being zero.

[0091] Experimental method:

[0092] During this experiment, we collected and sorted out multiple commonly used public datasets of low-light images, as well as two no-reference evaluation metrics for evaluating low-light image enhancement, and comprehensively evaluated the effectiveness of the present invention from both subjective vision and objective metrics.

[0093] Step 1: According to different low-light images input, obtain their corresponding illumination weight matrices, and use them to guide the adaptive initialization of the image illumination components.

[0094] Step 2: Run the program using Matlab, input the forensic frequency features extracted from the training set images and their corresponding labels into the KNN classifier to obtain a trained model.

[0095] Step 3: Under the constraint of the structured light prior, optimize and estimate the initial illumination components through the alternating direction minimization technique, and perform gamma correction on them to further perform non-linear adjustment on the image brightness.

[0096] Step 4: Perform gamma correction on the obtained optimized illumination components to further perform non-linear adjustment on the image brightness, and combine with the Retinex theory model to achieve the enhancement of low-light images.

[0097] Experiments prove that compared with the existing methods, the method proposed in the present invention has satisfactory enhancement effects and objective evaluation indicators in multiple commonly used public low-light image datasets, indicating the good effectiveness and generalization of the present invention. In addition, the present invention also has a certain enhancement effect on low-light videos.

[0098] The systems, devices, modules or units illustrated in the above embodiments can be specifically implemented by computer chips or entities, or by products with certain functions. A typical implementation device is a computer. Specifically, the computer can be, for example, a personal computer, a laptop computer, a cellular phone, a camera phone, a smart phone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or any combination of these devices.

[0099] It should also be noted that the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements not only includes those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. Without further limitation, the element defined by the statement "including one..." does not exclude the existence of additional identical elements in the process, method, commodity or device including the said element.

[0100] The above embodiments should be understood as being only used to illustrate the present invention and not to limit the protection scope of the present invention. After reading the content recorded in the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A low-light image enhancement method based on adaptive illumination initialization, characterized in that, it includes the following steps: (1) Collect and organize the existing publicly available low-light image datasets on the Internet; (2) According to different input low-light images, based on the proposed illumination adaptive initialization module, the illumination adaptive initialization module adaptively obtains the illumination weight matrix of the input image by considering the relevance of the local content information of the image, and accurately estimates the initial illumination component of the image; (3) Under the constraint of the structured illumination prior, optimize and estimate the initial illumination component by the alternating direction method of multipliers; (4) Perform gamma correction on the obtained optimized illumination component to achieve non-linear adjustment of the image brightness; (5) Combine the Retinex theory model to achieve the enhancement of low-light images; The step (2) estimates the initial illumination component of the image based on the proposed illumination adaptive initialization module according to different input images, specifically including: The typical image illumination initialization operations in the step (2) include taking the maximum value of the R, G, and B channels, taking the average value of the R, G, and B channels, and taking the V component in the HSV space, the H component represents hue, the S component represents saturation, and the V component represents brightness; The specific formula is expressed as follows: Among them, I 0 (x) is the initial illumination component, c includes three color channels of R, G, and B, and S c (x) is the maximum value component among the three color channels, which is the illumination weight matrix. Ω represents the local block centered on x. In this paper, the block size is taken as 3×3, and is the illumination adjustment parameter; The core idea of the Retinex theory model is to decompose the observed image into two parts: an illumination component and a reflectance component. The illumination component represents the distribution of illumination in the image scene and contains the structural information of the image; while the reflectance component represents the inherent properties of the object and is mainly represented by the texture details and color information of the image; its formula is specifically as follows: Among them, S(x) represents the input original low-light image, I(x) represents the illumination component, R(x) is the reflection component, x represents a specific pixel, and the operator represents the element-wise multiplication operation.

2. The low-light image enhancement method based on adaptive illumination initialization according to claim 1, characterized in that, the step (3) optimizes and estimates the initial illumination component by the alternating direction method of multipliers under the constraint of the structured illumination prior, specifically including: The ideal objective function of the image illumination component optimization algorithm is as follows: Among them, I 0 represents the initial illumination component, I represents the optimized illumination component, and W is the structural weight matrix. is the first-order derivative filter, which is specifically divided into the horizontal direction and the vertical direction in two parts, ||·|| 1 and ||·|| F are the 1-norm and the standard F-norm respectively. In the above objective function, the first term is the data fidelity term, which is used to constrain the difference between I 0 and I. The role of the regularization term is to limit the size of the solution space. The coefficient α is used to balance the fidelity term and the regularization term to achieve the structural-aware smoothing of the illumination component. The weight matrix W is designed to perceive the structural edge information of the image, specifically including the following horizontal direction W h (x) and the vertical direction W v (x) in two parts, specifically: Among them, G σ (x, y) represents a Gaussian kernel function with a standard deviation of σ, and there is dist(x, y) represents the spatial Euclidean distance between pixels x and y. ε is a very small constant to avoid the case where the denominator is zero, and |·| represents the absolute value operation; Perform an approximate simplification operation on the above objective function. First, expand the regularization term in the objective function to get, W d (x) is the structural weight matrix, and d therein includes the horizontal direction h and the vertical direction v; Here, is used to approximately replace the regular term Finally, the above formula is equivalently written in the following form: The coefficient α is used to balance the fidelity term and the regularization term to achieve the structure-aware smoothing of the illumination component; specifically, when is very small, is also relatively small, and the value of will also be suppressed.

3. The low-light image enhancement method based on adaptive illumination initialization according to claim 2, characterized in that, the step (4) performs gamma correction on the obtained optimized illumination component to achieve non-linear adjustment of the image brightness, and the specific formula is: I g (x) = I(x) γ Among them, γ takes a value of 0.

8. The final enhanced result S is obtained by combining the input image S(x) and the optimized illumination component I after illumination adjustment g , using the Retinex model out ; Here, ε is a very small constant to avoid the denominator being zero.

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