2021

[1]Xiaoguang Di [1]Chunhui Wang

[1]Harbin Institute of Technology, Harbin, 150001, China

2]South China University of Technology, Guangzhou, 510000, China

3]Mind Vogue Lab, Beijing, 100000, China

# Simplifying Low-Light Image Enhancement Networks with Relative Loss
Functions

Yu Zhang<EMAIL_ADDRESS><EMAIL_ADDRESS>Junde Wu
<EMAIL_ADDRESS>Yue Wang<EMAIL_ADDRESS>Yong Li<EMAIL_ADDRESS>Rao Fu
<EMAIL_ADDRESS>Yanwu Xu<EMAIL_ADDRESS>Guohui Yang<EMAIL_ADDRESS><EMAIL_ADDRESS>*  [  [

###### Abstract

Image enhancement is a common technique used to mitigate issues such as severe
noise, low brightness, low contrast, and color deviation in low-light images.
However, providing an optimal high-light image as a reference for low-light
image enhancement tasks is impossible, which makes the learning process more
difficult than other image processing tasks. As a result, although several
low-light image enhancement methods have been proposed, most of them are
either too complex or insufficient in addressing all the issues in low-light
images. In this paper, to make the learning easier in low-light image
enhancement, we introduce FLW-Net (Fast and LightWeight Network) and two
relative loss functions. Specifically, we first recognize the challenges of
the need for a large receptive field to obtain global contrast and the lack of
an absolute reference, which limits the simplification of network structures
in this task. Then, we propose an efficient global feature information
extraction component and two loss functions based on relative information to
overcome these challenges. Finally, we conducted comparative experiments to
demonstrate the effectiveness of the proposed method, and the results confirm
that the proposed method can significantly reduce the complexity of supervised
low-light image enhancement networks while improving processing effect. The
code is available at https://github.com/hitzhangyu/FLW-Net.

###### keywords:

Low-light Image, Image Enhancement, Lightweight Network, Relative Loss.

##  1 Introduction

Images captured in dark environments or with insufficient exposure often
become low-light images that suffer from low contrast, low brightness, severe
noise, and color deviation, making some information in the images invisible.
To improve the quality of these images, numerous low-light image enhancement
methods have been proposed in recent years (C. Guo ., 2020; Y. Jiang ., 2021;
Y. Zhang, Guo ., 2021; Ma ., 2022; X. Liu, Xie ., 2023). Although these
methods have shown promising results, there remains a trade-off between
processing speed and effect, regardless of whether they are based on learning
or not.

While non-learning-based low-light image enhancement methods are capable of
significantly improving image contrast and brightness(X. Guo ., 2016; Kimmel
., 2003; Yu Zhu, 2019; Lee ., 2013), subsequent separate denoising steps
(Dabov ., 2007) or joint iterative denoising processes based on variation (M.
Li ., 2018) can be time-consuming. This limitation makes most of these methods
unsuitable for real-time low-light image enhancement applications.

Learning-based low-light image enhancement methods can be categorized into two
main groups: the supervised learning-based and the unsupervised learning-
based. Typically, unsupervised learning-based methods are lightweight and are
more robust to various environments (C. Guo ., 2020; C. Li ., 2021; Ma .,
2022). However, they often lack responsive color correction and denoising
methods, which limits their ability to improve the accuracy of subsequent
high-level tasks (Y. Zhang ., 2022). In contrast, supervised learning-based
methods are designed to address all types of low-light image degradation and
can significantly improve image quality (N. Jiang ., 2023; K. Zhang ., 2023;
Zhou ., 2023). However, most of these methods require a complex network
structure, resulting in longer processing times.

Designing a lightweight network that can simultaneously enhance contrast and
remove noise is a challenging task. Two primary challenges limit the
simplification of the network. Firstly, the contrast adjustment of an image
should consider both local and global information. This requires a large
receptive field to capture global contrast, which increases the complexity of
the network. Secondly, in low-light image enhancement, there is no absolute
reference, which means the network must learn uncertain output values for the
same input pixel or image block during denoising (We can name it the one-to-
many problem). That makes it more difficult for supervised learning-based
methods to learn compared to unsupervised learning-based methods, since most
unsupervised learning-based methods have a consistent assumption about the
output value, such as the average brightness value being close to a fixed
value(C. Li ., 2021).

Figure 1: Visual comparison with some SOTA methods. (a) The original input
low-light image. (b) to (e) are enhanced images produced by Zero-DCE++ (C. Li
., 2021), KIND++ (Y. Zhang, Guo ., 2021) and the proposed method in this
paper. (f) The reference image. It can be seen that the color of the enhanced
image (e) produced by our proposed method is the closest to that of the
reference image (f).

In this paper, to address these challenges, we propose a solution by
introducing a fast and lightweight image enhancement network called FLW-Net,
along with two specially designed loss functions based on relative information
for the low-light image enhancement task. We can abbreviate the losses based
on relative information as the relative losses, and relative losses can
achieve an extremum when the reference and the output are similar in some
features, rather than requiring them to be exactly equal. An example of
enhancing a low-light image comprising color deviation is shown in Fig. 1. It
can be seen that the color of the enhanced image produced by proposed method
is the closest to that of the reference image.

Specifically, in terms of network structure design, we propose a simple Global
Feature Extraction (GFE) component that can extract global information from
the image’s histogram and generate a global brightness adjustment proposal
through a higher-order curve adjustment method (C. Guo ., 2020). In terms of
loss functions, we propose two losses based on relative information to
alleviate the one-to-many problem in low-light image enhancement task.

Our contributions can be summarized as follows:

  * •

To improve computational efficiency by utilizing fewer parameters for
obtaining global information, we proposed a Global Feature Extraction (GFE)
component with only $1.4$K parameters. Unlike most existing methods that use
large receptive fields or Transformer structures for extracting global
information, GFE extracts information from histograms with a small number of
bins. This not only makes it more efficient but also allows for easier
integration with hyperparameters that control the degree of global
enhancement.

  * •

To address the learning difficulty caused by multiple potential reference
images, we proposed two novel loss functions ($L_{brightness}$ and
$L_{structure}$) based on relative information. Unlike traditional $L_{1}$ or
$L_{2}$ losses that aim to make the enhanced image exactly match the reference
image, our proposed loss functions utilize cosine similarity, allowing for
brightness differences between the output and reference. Then the network can
focus more on color, structure and noise removal. When the proposed loss
functions are combined with other supervised methods, it can achieve better
quantitative metrics with less parameters(e.g., only about $5\%$ parameters of
the original KIND’s network when combined with KIND (Y. Zhang ., 2019)).

  * •

With GFE and two proposed loss functions, we built a fast and lightweight low-
light image enhancement network, named FLW-Net, which achieves comparable or
even better performance compared to state-of-the-art methods while maintaining
faster processing speed. This shows the potential of reducing the complexity
of low-light image enhancement networks with the proposed methods.

##  2 Related Work

###  2.1 Low-Light Image Enhancement

Non-learning-based low-light image enhancement solutions mainly include
histogram equalization, gamma correction, methods based on dehazing (Dong .,
2011) or the Retinex model (S. Wang ., 2013), as well as other improved
methods based on these approaches (Celik Tjahjadi, 2011; X. Guo ., 2016; Park
., 2017; G. Fu ., 2019; Kumar Bhandari, 2022). Although these methods can
significantly improve the brightness and contrast of images, removing noise
and restoring color remain challenging.

Recently, learning-based methods for enhancing low-light images have achieved
promising results, including supervised methods (Y. Zhang ., 2019; Y. Zhang,
Guo ., 2021; Y. Zhang ., 2022; Xu ., 2022) and unsupervised methods (C. Guo .,
2020; Xiong ., 2020; Y. Jiang ., 2021; Y. Zhang, Di ., 2021; Ma ., 2022; X.
Liu, Ma ., 2023). However, unlike other image processing or computer vision
tasks, the low-light image enhancement task usually lacks an ground-
truth/absolute label. For the same scene, there may be multiple low-light and
high-light images, making it difficult to determine which reference image is
the best. Even after expert correction, it can still be challenging to select
the ideal reference image (Y. Zhang, Guo ., 2021; Y. Zhang ., 2022).

Therefore, most supervised methods for low-light image enhancement often face
challenges due to the presence of multiple potential reference images. To
address this issue, there are mainly two types of methods. The first involves
designing complex networks, such as the current state-of-the-art method MAXIM
(Tu ., 2022). While these methods can achieve promising visual results, they
are often time-consuming for low-light image enhancement tasks.

The second type of method involves connecting the input and output during
training by introducing hyperparameters (Chen ., 2018; Q. Fu ., 2020),
simplified Retinex models (Wei ., 2018), or both (Y. Zhang ., 2019). For
instance, Chen . (2018) introduced the exposure time ratio of reference and
input images as a hyperparameter to achieve denoising and color restoration.
Q. Fu . (2020) further proposed a sub-network to automatically select
hyperparameters. Wei . (2018) incorporated the simplified Retinex model into
the network. However, the assumption in the simplified Retinex model that all
three color channels have the same illumination image does not align with
reality (Y. Zhang ., 2022), leading to suboptimal denoising effects.

To address this issue, Y. Zhang . (2019) and Y. Zhang, Guo . (2021) introduced
both hyperparameters and the simplified Retinex model into the network and
designed a separate restoration module to remove noise and correct color in
the reflection image. However, it is important to note that the introduction
of both Retinex models and hyperparameters might still deviate from the real
imaging process. Consequently, while these methods involve less complex
network structures, their running time may not meet the requirements of
practical applications.

Unsupervised methods for low-light image enhancement typically assume that the
output meets certain constraints, making them more lightweight and more stable
for unseen scenes. For example, C. Guo . (2020) use the mean value assumption
(e.g., supposing the mean brightness of the image is between 0.4 and 0.6) and
some specially designed loss functions to constrain the output. Xiong . (2020)
specify the initial value of the illumination image in the simplified Retinex
model as the max value of R,G,B in each pixel. Y. Jiang . (2021) propose to
learn constraints on the output from the normal-light images through GAN
framework. Ma . (2022) proposed to constrain the similarity of outputs at
different stages during training. Although most of these unsupervised methods
can meet real-time requirements, accurately removing noise and restoring color
remains a challenge due to the lack of sufficient noise and color constraints.

By comparing supervised and unsupervised methods, it can be observed that if
we do not aim to achieve enhancement results that are identical to the
reference image but rather focus on learning color, structure, and noise
removal from the reference image, it is possible to utilize a simple network
to effectively remove noise and restore colors during image enhancement. At
this point, the problem to be addressed is how to design evaluation metrics or
loss functions that are not affected by brightness differences.

###  2.2 Image Retouching

Image retouching methods focus on problems such as inappropriate brightness,
poor contrast, color deviation, etc., similar to image enhancement tasks (Y.
Wang, Li ., 2022). However, most of these methods do not consider the noise
problem. Therefore, basic retouching operations can work on a single pixel,
making them extremely fast and lightweight (He ., 2020; Y. Liu ., 2022; Zeng
., 2020; Y. Wang, Li ., 2022). For example, He . (2020) and Y. Liu . (2022)
proposed the Conditional Sequential Retouching Network (CSRNet) with only 37K
trainable parameters. Y. Wang, Li . (2022) proposed the trainable neural color
operators, which contains only 28K parameters in their method. The successful
applications of simple networks in image retouching also demonstrate the
feasibility of using simple networks for image enhancement tasks.

Figure 2: The detailed structure of the proposed method.

##  3 Methodology

Figure 2 illustrates the architecture of FLW-Net, which comprises two primary
modules: the Global Feature Extraction (GFE) component and the Local
Enhancement Network (LEN) component. The GFE component takes the low-light
image’s V channel and the desired average brightness as inputs and produces a
global brightness adjustment proposal through higher-order curve adjustment
method. Then, the proposal is concatenated and fed into LEN. The LEN component
takes the low-light image and the global brightness adjustment proposal as
inputs and enhances the image with some carefully designed loss functions. It
consists of several convolutional layers with a local receptive field to
capture local information and generate high-frequency details.

The proposed method includes several loss functions beyond the commonly used
$L_{1}$ and SSIM. The color loss, denoted as $L_{color}$, is used to measure
the color similarity between the enhanced image and the reference image. The
brightness loss, denoted as $L_{brightness}$, is used to measure the
difference in brightness orders between the enhanced image and the reference
image. Finally, the structure loss, denoted as $L_{structure}$, is designed to
encourage the enhanced image to have similar gradient orders to the reference
image. We refer to these losses as relative losses.

Unlike in $L_{1}$ and SSIM losses, where the extremum is only reached when the
output and reference are exactly equal, the relative loss can achieve the
extremum when the output and reference share some common features. All of
these loss functions, including the $L_{1}$ and SSIM loss, are combined to
form the total loss function used in training the FLW-Net. To the best of our
knowledge, $L_{brightness}$ and $L_{structure}$ are first proposed by this
paper in this low-light image enhancement task.

###  3.1 Global Feature Extraction Component

It is unnecessary to emphasize the importance of global information extraction
in low-light image enhancement, as it has been extensively discussed in
previous literature (Cui ., 2022). However, the challenge lies in efficiently
extracting global information and integrating it into the enhancement network.

Y. Zhang . (2022) has proven that the V channel in the HSV color space is
sufficient to represent the brightness of the input low-light image.
Meanwhile, C. Guo . (2020) proposed to iteratively apply Equation (1) to
adjust the input low-light image.

$\mathbf{I_{k+1}}=\mathbf{I_{k}}+\alpha_{k}\mathbf{I_{k}}(1-\mathbf{I_{k}})$
(1)

where $k$ represents the number of iterations (e.g., $\mathbf{I_{0}}$
represents the input low-light image).

Inspired by those two works, we propose to extract global information from the
histogram of the V channel of the low-light image and represent it as higher-
order curve coefficients, denoted as $\alpha_{0,1,...t}$. Specifically,

$\\{\alpha_{0,1,...t}\\}=G(H(\mathbf{I^{v}}))$ (2)

where $\mathbf{I^{v}}$ represents the V channel of the low-light image
$\mathbf{I}$ in the HSV color space, $H(\mathbf{I^{v}})$ represents the
operation of obtaining the histogram of the image $\mathbf{I^{v}}$, and
$G(\cdot)$ represents the Global Feature Extraction (GFE) component, which is
implemented using a Five-layer Multi-Layer Perception with only $1.4$K
parameters. Compared with the method of C. Guo . (2020), the GFE component in
our proposed method extracts global information from the histogram of the V
channel instead of at the pixel level, which is more efficient. Specifically,
the computational cost of the GFE component does not significantly increase
with the increase in image size. Additionally, the output of GFE component is
not the final enhanced result, which allows for further denoising and color
restoration. Compared with the method of Y. Zhang . (2022), the proposed
method does not need to be combined with other image contrast enhancement
methods and can achieve end-to-end training with the help of the loss
functions proposed in Eqn. (9) and Eqn. (11).

As mentioned, there is currently no definitive standard that defines whether
an enhancement result is optimal. Similarly, we cannot claim that the
processing result of a fixed-parameter network trained on a specific dataset
is optimal. In this case, introducing adjustable parameters for image
enhancement is a reasonable solution, as adopted in previous work (X. Liu, Xie
., 2023; Y. Zhang, Guo ., 2021; Y. Wang, Wan ., 2022). Additionally, if the
parameters are related to reference images, we can allow the network to learn
relatively deterministic mapping operations, thereby simplifying the training
difficulty of the network in the training phase.

The GFE component can be easily modified to incorporate additional
hyperparameters. In this paper, we used the desired average brightness value,
$\mu$, as the hyperparameter. During the training process, $\mu$ is calculated
as the mean value of the V channel of the reference image. Compared to
previous works which utilized parameters such as exposure time difference
between reference images and input (Chen ., 2018), and brightness ratio
between the illumination image of the reference image and that of the input
image (Y. Zhang ., 2019), $\mu$ is more intuitive and highly correlated with
histogram information. Moreover, during the testing process, we can easily fix
$\mu$ to a constant value, as done in some unsupervised works(C. Guo ., 2020).
Therefore, the modified GFE component can be expressed as:

$\\{\alpha_{0,1,...t}\\}=G(H(\mathbf{I^{v}}),\mu)$ (3)

Then, we can iteratively adjust the V channel of the low-light image to obtain
the global brightness adjustment proposal, as follows:

$\mathbf{I^{v}_{k+1}}=\mathbf{I^{v}_{k}}+\alpha_{k}\mathbf{I^{v}_{k}}(1-\mathbf{I^{v}_{k}})$
(4)

After obtaining the global brightness adjustment proposal, it will be
concatenated with the middle layer of LEN and fed into the LEN for further
enhancement. The entire FLW-Net is trained end-to-end, which means that all
the components are trained jointly to optimize the overall performance of the
network.

###  3.2 Loss Functions based on Relative Information

Let us consider $\\{\mathbf{I},\mathbf{Y}\\}$ as one paired low/high-light
images. Typically, we use lots of paired images to train the enhancement
network $E$ and hope it can well fit the following Equation (5):

$\mathbf{Y_{(i,j)}}=E(\mathbf{I_{(i,j)}})$ (5)

where $(i,j)$ represents the coordinate of one pixel. To achieve this, various
loss functions have been adopted to train the enhancement network $E$ with
paired low/high-light images, including commonly used $L_{1}$, $L_{2}$ and
SSIM loss, etc. However, due to the one-to-many problem, these loss functions
may not be as effective for image enhancement as they are for other low-level
image processing tasks such as image denoising, image deblurring, and image
dehazing. In other words, these loss functions are more suitable for learning
the mapping relationship with an absolute reference image for the input.

As previously mentioned, previous studies have proposed strategies to
establish a one-to-one relationship between the input and output of the
enhancement models (where one input low-light image corresponds to one certain
reference image). However, the Retinex models and additional parameters
adopted in those work cannot onvert the one-to-many problem into a real one-
to-one problem. In practice, even adding a hyperparameter for each pixel does
not guarantee a satisfactory color restoration effect(Y. Zhang ., 2022).
Therefore, most of previous works often require complex networks or separate
denoising modules, such as SID (Chen ., 2018), RetinexNet (Wei ., 2018), KinD
(Y. Zhang ., 2019), KinD++ (Y. Zhang, Guo ., 2021).

Since there is no absolute supervision information, one intuitive approach is
to use relative information in the loss functions, which reduces the
assumption of existence of absolute reference images. Previous unsupervised
methods have proposed some useful loss functions, such as spatial consistency
loss (C. Guo ., 2020), normalized gradient error (Y. Zhang, Di ., 2021), and
perception loss (Y. Jiang ., 2021). However, most of them do not achieve
impressive results in supervised methods, since they impose weak constraints.

In this paper, we propose the use of relative losses, which are loss functions
based on relative information, to make the learning easier for networks.

Firstly, for one pixel, we expect its color information more than the
brightness to match the reference image. To achieve this, we need to extract
the image’s color information, which can be accomplished through various color
spaces, such as the HSV (Hue, Saturation, Value) or HSI (Hue, Saturation,
Intensity) color space. In this paper, we chose to use the HSV color space. It
has been demonstrated that two pixels share the same Hue and Saturation when
they satisfy the following equation (Y. Zhang ., 2022):

$E\mathbf{(I_{(i,j)})}=\lambda\mathbf{Y_{(i,j)}}$ (6)

where $\lambda$ represents arbitrary non-zero positive number. It should be
noticed that both $E\mathbf{(I_{(i,j)})}$ and $\mathbf{Y_{(i,j)}}$ represent
3D vectors. Then, we can adopt the cosine similarity to measure the Hue and
Saturation difference between two pixels. Therefore, the loss function for
color can be designed as follows:

$L_{color}=1-\sum_{i=1,j=1}^{m,n}<E\mathbf{(I_{(i,j)})},\mathbf{Y_{(i,j)}}>$
(7)

where $<\cdot,\cdot>$ represents the cosine similarity of two vectors. By
minimizing this loss function, the network is encouraged to match the Hue and
Saturation information between the output and reference images. This loss
function has also been adopted in many other image enhancement (C. Liu .,
2022; K. Zhang ., 2023) and Computational Color Constancy work (Barnard .,
2002; Gijsenij ., 2011).

Secondly, regarding the brightness, it is expected that the enhanced images
have the same lightness order as the reference (S. Wang ., 2013), which means
that images that are brighter in the reference should also be brighter in the
enhanced image. S. Wang . (2013) proposed the evaluation metric, LOE
(Lightness-Order-Error), for the lightness order error. However, directly
incorporating LOE into the loss function is not straightforward since it is
difficult to calculate the corresponding gradients in back propagation. In
this paper, we propose the following equation to model the brightness relation
between the enhanced image and the reference.

$b(E\mathbf{(I_{(i,j)})})=\beta b(\mathbf{Y_{(i,j)}})+\gamma$ (8)

where $b(\cdot)$ represent image blocks centered on pixels
$E\mathbf{(I_{(i,j)})}$ and $\mathbf{Y_{(i,j)}}$, $\beta$ and $\gamma$ can
represent 3D vectors for color image or scalars in gray images. For different
blocks, there can be different $\beta$ and $\gamma$. This is useful for
processing images with non-uniform brightness, where different regions of the
image have different enhancement levels. It can be seen that, in this model,
the enhanced images have the same lightness order as the reference image in
every image block. Also, it is more rigorous than the LOE metric since it
requires more than just brightness order. Specifically, it requires the
enhanced image to be a linear transformation of the noise-free reference
image, which significantly suppresses noise. Then, we can design the loss
function as follows:

$\displaystyle L_{brightness}$
$\displaystyle=1-\sum_{c\in{{R,G,B}}}\sum_{i=1,j=1}^{m,n}$
$\displaystyle<b(E\mathbf{(I^{c}_{(i,j)})})-min(b(E\mathbf{(I^{c}_{(i,j)})})),$
$\displaystyle b(\mathbf{Y^{c}_{(i,j)}})-min(b(\mathbf{Y^{c}_{(i,j)}}))>$ (9)

where $c$ represents the different color channels, and the purpose of
subtracting the minimum value is to remove the influence of the constant
$\gamma$. The following experimental results show that $L_{brightness}$ can
improve the PSNR metric which is related to noise suppression(In Sec. 4.3,
Table 4 and Figure 9).

Thirdly, for the structure information, it is usually expressed by gradient
information. We can adopt a similar model as Equation (8). The difference is
replacing the brightness value with gradient. Then, we can get the following
Equation (10).

$b(\nabla E\mathbf{(I_{(i,j)})})=\eta b(\nabla\mathbf{Y_{(i,j)}})+\epsilon$
(10)

Then, the loss funciton for structure can be expressed as follows:

$\displaystyle L_{structure}$
$\displaystyle=1-\sum_{c\in{{R,G,B}}}\sum_{i=1,j=1}^{m,n}$
$\displaystyle<b(\nabla E\mathbf{(I^{c}_{(i,j)})})-min(b(\nabla
E\mathbf{(I^{c}_{(i,j)})})),$ $\displaystyle
b(\nabla\mathbf{Y^{c}_{(i,j)}})-min(b(\nabla\mathbf{Y^{c}_{(i,j)}}))>$ (11)

If we remove the $\epsilon$ part in Eqn.(10), Eqn.(10) will become the
derivative of the Eqn.(8). At this point, $L_{brightness}$ and $L_{structure}$
will essentially represent the same thing. However, by introducing $\epsilon$
in Eqn.(10), it will allow for non-linear changes in brightness within image
blocks. This more closely aligns with the imaging process in reality and can
reduce the effects of saturation and under-saturation caused by linear changes
in brightness during enhancement. As a result, $L_{structure}$ is more
effective in preserving image structures. Experimental results also indicate
that it is more effective in improving the structural similarity index (SSIM)
metric(In Sec. 4.3, Table 4 and Figure 9).

The total loss can be expressed as follows:

$L_{ALL}=L_{1}+L_{SSIM}+L_{color}+L_{brightness}+L_{structure}$ (12)

where $L_{SSIM}$ represents the SSIM loss between the enhanced and reference
images.

Figure 3: Visual comparison results on LOL-V1 dataset. Comparison methods
include Zero-DCE++, LIME, KIND, KIND++, DecNet, PairLIE, RetienxNet, IAT and
the proposed FLW-Net trained on LOL-V1 and LOL-V2 datasets. (Best viewed on
high-resolution displays with zoom-in.)

##  4 Experiments

###  4.1 Implementation Details

The framework is implemented with PyTorch on an NVIDIA 3090 Ti GPU. The batch
size used for training is 171. We use the Adam optimizer to train the network
with a learning rate of 0.0001. We mainly use two datasets for training and
testing: the LOL-V1 dataset (Wei ., 2018) and the LOL-V2 dataset (Yang .,
2021). The LOL-V1 dataset contains 500 image pairs, with 15 pairs used for
testing. The LOL-V2 dataset contains 689 image pairs for training and 100
pairs for testing. We also collected some images online and merged them
together, which we refer to as the Mixed dataset. The Mixed dataset includes
the test images of LOL-V1 (15 images), LIME (X. Guo ., 2016) (10 images), MF
(X. Fu ., 2016) (10 images), and
VV111https://sites.google.com/site/vonikakis/datasets/challenging-dataset-for-
enhancement (23 images), and most of these images do not have corresponding
reference images.

We used four metrics for quantitative comparison: PSNR, SSIM, CIEDE2000 (Luo
., 2001; Sharma ., 2005), and NIQE (Mittal ., 2012). PSNR and SSIM are
reference image quality assessment methods that indicate the noise level and
the structural similarity between the enhanced images and the reference,
respectively. CIEDE2000 is a reference image quality assessment method to
accurately measure colors differences, which is published by International
Commission on Illumination(Also known as the Commission Internationale de
l´Eclairage, CIE), and a lower value indicates less color difference. NIQE is
a non-reference image quality assessment method that evaluates the naturalness
of the image, and a lower value indicates better quality. To differentiate
between the $\mu$ values during the training and testing processes, we use
$\mu_{train}$ and $\mu_{test}$ to represent them, respectively.

###  4.2 Objective Performance Evaluation

In this section, we compared our method with several state-of-the-art (SOTA)
low-light image enhancement methods, including LIME (X. Guo ., 2016),
RetinexNet (Wei ., 2018), Zerodce++ (C. Li ., 2021), KIND (Y. Zhang ., 2019),
KIND++ (Y. Zhang, Guo ., 2021), DecNet (X. Liu, Xie ., 2023), PairLIE (Z. Fu
., 2023) and IAT (Cui ., 2022). Among them, LIME is a non-learning-based
method, and ZeroDCE++ can be trained without any references. PairLIE can be
trained with paired low-ligh images. The other methods are based on supervised
learning. Among them, KIND (Y. Zhang ., 2019), KIND++(Y. Zhang, Guo ., 2021)
and DecNet(X. Liu, Xie ., 2023) all have hyperparameters during training and
testing. The comparison results are shown in Table 1, 2 and 3 and Figures 3,
4, 5 and 6. In Fig. 5 and 6, the hyperparameter $\mu$ is fixed at a constant
value of 0.4.

During the training on the LOL-V1 dataset, we utilized only 343 images, which
is approximately half of the LOL-V2 training data. It should be noted that
both datasets were produced by the same team, and LOL-V2 contains most of the
data in LOL-V1. Hence, we can evaluate the impact of training data volume on
the network.

As shown in Table 1, the training data volume has a greater impact on PSNR
than SSIM. For instance, when trained on the LOL-V1 dataset, the PSNR reduced
by almost 0.9 dB compared to the LOL-V2 dataset (PSNR: $26.61\rightarrow
25.71$). However, the SSIM only decreased by 0.01 (SSIM: $0.88\rightarrow
0.87$). Furthermore, irrespective of whether trained on the LOL-V1 or LOL-V2
dataset, FLW-Net outperforms other methods in terms of PSNR. Regarding SSIM,
FLW-Net, KIND, and KIND++ achieve similar results. However, FLW-Net has fewer
parameters (only 17K parameters) and consumes less running time during
testing. It should be noted that when testing on the LOL-V2 and LOL-V1
datasets, the hyperparameters of DecNet, KIND and KIND++ are derived from the
reference image.

Table 1: Quantitative comparison results on LOL (V1 (Wei ., 2018) & V2 (Yang
., 2021)) datasets and a mixed dataset. The mixed dataset includes the test
images of LOL-V1 (15 images), LIME (X. Guo ., 2016) (10 images), MF (X. Fu .,
2016) (10 images), and VV (23 images), and most of these images do not have
corresponding reference images. It should be noted that the test time of KIND
and KIND++ comes from KIND++(Y. Zhang, Guo ., 2021) with a Titan-X GPU, and
the test time of RetinexNet does not include the running time of BM3D(Dabov .,
2007) for denoising.

Method | LOL-V1 | LOL-V2 | Mixed Dataset(Unpaired) | Efficiency
---|---|---|---|---
PSNR$\uparrow$ | SSIM$\uparrow$ | NIQE$\downarrow$ | PSNR$\uparrow$ | SSIM$\uparrow$ | NIQE$\downarrow$ | NIQE$\downarrow$ | Params(M)$\downarrow$ | test time(s)$\downarrow$
LIME(X. Guo ., 2016) | 17.22 | 0.50 | 5.32 | 15.77 | 0.46 | 5.37 | 4.57 | - | 0.190
RetinexNet(Wei ., 2018) | 17.86 | 0.78 | 6.37 | 17.37 | 0.76 | 9.09 | 5.68 | 0.4 | 0.019∗
Zerodce++(C. Li ., 2021) | 15.35 | 0.57 | 7.86 | 18.49 | 0.58 | 8.05 | 4.53 | 0.01 | 0.001
KIND(Y. Zhang ., 2019) | 20.38 | 0.83 | 5.45 | 23.78 | 0.88 | 4.96 | 3.87 | 8.21 | 0.11∗
KIND++(Y. Zhang, Guo ., 2021) | 21.80 | 0.84 | 5.17 | 22.21 | 0.84 | 4.89 | 3.74 | 8.28 | 0.12∗
IAT(Cui ., 2022) | 23.38 | 0.81 | 3.92 | 23.50 | 0.82 | 4.29 | 4.71 | 0.09 | 0.004
DecNet(X. Liu, Xie ., 2023) | 22.49 | 0.82 | 4.51 | 22.56 | 0.84 | 4.83 | 4.26 | 1.83 | 0.353
PairLIE(Z. Fu ., 2023) | 18.47 | 0.75 | 4.25 | 19.88 | 0.78 | 4.34 | 3.90 | 0.33 | 0.057
FLW(Training on LOL V1) | 23.84 | 0.83 | 4.22 | 25.71 | 0.87 | 4.09 | 3.93 | 0.02 | 0.001
FLW(Training on LOL V2) | 24.70 | 0.84 | 4.11 | 26.61 | 0.88 | 3.89 | 3.72 | 0.02 | 0.001

Figure 4: Visual comparison results on LOL-V2 dataset. Comparison methods
include Zero-DCE++, LIME, KIND, KIND++, DecNet, PairLIE, RetienxNet, IAT and
the proposed FLW-Net trained on LOL-V1 and LOL-V2 datasets. (Best viewed on
high-resolution displays with zoom-in.)  Table 2: Color comparison results on
LOL (V1 (Wei ., 2018) & V2 (Yang ., 2021)) datasets.

Method | CIEDE2000$\downarrow$
---|---
LOL-V1 | LOL-V2
LIME(X. Guo ., 2016) | 14.62 | 17.63
RetinexNet(Wei ., 2018) | 13.76 | 18.07
Zerodce++(C. Li ., 2021) | 19.28 | 14.27
KIND(Y. Zhang ., 2019) | 9.68 | 6.74
KIND++(Y. Zhang, Guo ., 2021) | 8.51 | 9.36
IAT(Cui ., 2022) | 7.97 | 8.17
DecNet(X. Liu, Xie ., 2023) | 8.93 | 8.87
PairLIE(Z. Fu ., 2023) | 11.93 | 11.23
FLW(Training on LOL V1) | 7.74 | 6.64
FLW(Training on LOL V2) | 7.23 | 6.06

Table 2 presents the color comparison results of various methods on the LOL
(V1 (Wei ., 2018) $\&$ V2 (Yang ., 2021)) datasets. We used the total color
difference $\Delta E_{00}$ in CIEDE2000 to evaluate different methods. As can
be observed, the proposed method achieved lower CIEDE2000($\Delta E_{00}$)
values than other methods, demonstrating the effectiveness of our proposed
method in color restoration.

Figure 5: Visual comparison results on MF dataset (X. Fu ., 2016). Comparison
methods include Zero-DCE++, LIME, KIND, KIND++, DecNet, PairLIE, RetienxNet,
IAT and the proposed FLW-Net trained on LOL-V1 and LOL-V2 datasets. (Best
viewed on high-resolution displays with zoom-in.)  Figure 6: Visual comparison
results on image from Internet. Comparison methods include Zero-DCE++, LIME,
KIND, KIND++, DecNet, PairLIE, RetienxNet, IAT and the proposed FLW-Net
trained on LOL-V1 and LOL-V2 datasets. (Best viewed on high-resolution
displays with zoom-in.)  Figure 7: Visual comparison results on MF dataset
when we change the $\mu_{test}$ value from $0.1$ to $0.9$ with a step of 0.1.
(Best viewed on high-resolution displays with zoom-in.) Figure 8: Visual
comparison results on LIME dataset when we change the $\mu_{test}$ value from
$0.1$ to $0.9$ with a step of 0.1.(Best viewed on high-resolution displays
with zoom-in.)  Table 3: Comparison results on LOL-V2 (Yang ., 2021)) datasets
with fixed hyperparameter in all methods during test. ($\mu_{test}=0.4$ is
adopted in our method)

Method$\uparrow$ | PSNR$\uparrow$ | SSIM | NIQE$\downarrow$ | CIEDE2000$\downarrow$
---|---|---|---|---
KIND(Y. Zhang ., 2019) | 20.59 | 0.82 | 4.86 | 9.3872
KIND++(Y. Zhang, Guo ., 2021) | 17.66 | 0.77 | 4.73 | 13.89
DecNet(X. Liu, Xie ., 2023) | 21.13 | 0.83 | 4.85 | 10.45
FLW(Ours) | 23.50 | 0.86 | 3.88 | 8.28

In Figures 3 and 4, we can observe that the images enhanced by FLW-Net are
more closely aligned with the reference images in terms of brightness,
contrast, and color. The models used in LIME and RetinexNet are simplified
Retinex models. Therefore, the Saturation and Hue of the enhanced images are
identical to those of the original low-light images, especially in Figure 4.
Although KIND and KIND++ introduced a restoration network to recover the color
and remove noise in the reflection image, the results are still not stable.
For instance, in Figure 4(e), the image enhanced by KIND++ still has color
deviations compared with the reference image. In Figure 5(d), the small light
source was treated as noise and removed by KIND.

During testing, the value of $\mu_{test}$ can be obtained from reference
images such as (Y. Zhang ., 2019), (X. Liu, Xie ., 2023), and (Y. Zhang, Guo
., 2021). However, in practical applications, the value of $\mu_{test}$ is
typically determined by the user or machine to dynamically adjust enhancement
results, rather than relying on the reference image. Therefore, it is
important to carefully consider the impact of $\mu_{test}$ values. In this
regard, we also present the results obtained when $\mu_{test}$ takes on
constant values during testing.

Table 3 shows the quantitative comparison results with other methods which
also introduces hyperparameter, and it can be seen that the proposed method
can achieve better performance than other methods with less parameters and
simpler network structure. Fig. 5 and 6 shows the visual comparison results
with other methods. It can be seen that, the proposed method can effectively
remove noise while preserving structural information.

###  4.3 Ablation Study

We performed two ablation studies on the LOL-V2 dataset to demonstrate the
effectiveness of each component in our proposed method. For quantitative
comparison, we used the evaluation metrics of PSNR, SSIM and CIEDE2000.

Contribution of Each Loss: In this ablation study, we used the complete
network trained with $L_{1}$ and SSIM loss as the baseline model. We then
incorporated the relative loss functions into the network’s loss function and
retrained it to examine their effects on the performance of the model.
Additionally, we also trained the network solely with the relative loss
functions to evaluate their effectiveness.

In Table 4, it can be observed that the addition of each relative loss to the
baseline model leads to a slight improvement in PSNR or SSIM when $\mu_{test}$
is obtained from reference images. However, when $\mu_{test}$ takes on a
constant value for all testing images, both $L_{brightness}$ and
$L_{structure}$ demonstrate significant improvements in PSNR and SSIM. This
demonstrates that the proposed two loss functions can help the network better
learn noise removal and structural preservation, enhancing the stability of
the network. Between these two losses, $L_{brightness}$ shows a better
improvement in PSNR, which is related to its denoising ability, while
$L_{structure}$ shows a better improvement in SSIM, which is related to its
ability to retain structural information. On the other hand, the improvement
in PSNR and SSIM with $L_{color}$ is relatively minor. This could be because
$L_{color}$ only considers the information of a single pixel, whereas noise
removal and retention of structural information require the introduction of
information from surrounding pixels.

Table 4: The influence of different training losses. During testing, the input
$\mu_{test}$ value can be a constant (e.g., $\mu_{test}=0.4$) or obtained
through the reference(e.g., $\mu_{test}$ equals the mean value of the
reference’s V channel).

Loss functions | $\mu_{test}=0.4$ | $\mu_{test}$ from reference
---|---|---
$L_{1}$+SSIM | $L_{color}$ | $L_{brightness}$ | $L_{structure}$ | PSNR$\uparrow$ | SSIM$\uparrow$ | CIEDE2000$\downarrow$ | PSNR$\uparrow$ | SSIM$\uparrow$ | CIEDE2000$\downarrow$
✓ |  |  |  | 22.62 | 0.84 | 8.67 | 26.26 | 0.87 | 6.20
| ✓ | ✓ | ✓ | 20.54 | 0.83 | 10.60 | 21.22 | 0.84 | 9.85
✓ | ✓ |  |  | 22.88 | 0.85 | 8.37 | 26.49 | 0.87 | 5.92
✓ |  | ✓ |  | 23.72 | 0.85 | 7.90 | 26.80 | 0.87 | 5.86
✓ |  |  | ✓ | 23.28 | 0.86 | 8.14 | 26.75 | 0.88 | 5.84
✓ | ✓ | ✓ | ✓ | 23.50 | 0.86 | 8.28 | 26.61 | 0.88 | 6.06

Furthermore, as shown in Table 4, all three loss functions based on relative
information can lead to improvements in color restoration performance. Among
them, the proposed $L_{brightness}$ and $L_{structure}$ demonstrate better
color restoration performance than the commonly used $L_{color}$. However,
when we use all three loss functions simultaneously, the performance of the
CIEDE2000 metric does not reach its optimum. This may be due to conflicts
between the assumptions of the models used by the three loss functions. The
same issue is also reflected in the PSNR metric. When we only add
$L_{brightness}$ to the loss functions, the PSNR value can reach $23.72$ and
$26.80$, while when we add all three loss functions simultaneously, the PSNR
value can only reach $23.50$ and $26.61$.

Fig. 7 and 8 show the impact of different $\mu_{test}$ values on the
enhancement results. It can be seen that, as $\mu_{test}$ value changes, the
enhanced images’ brightness change accordingly. This indicates that the
strategy of using the parameter $\mu_{test}$ to control the enhancement
results is feasible.

Figure 9: Influence on PSNR and SSIM of different loss functions when changing
the $\mu_{test}$ value. (a) The PSNR with different $\mu_{test}$ values. (b)
The SSIM with different $\mu_{test}$ value. ALL loss means that all loss
functions are added with the same weight (Equation (12)).

The brightness differences have a significant influence on PSNR and SSIM
values. Fig. 9 shows the changes in SSIM and PSNR values with different
$\mu_{test}$ values and loss functions. It can be seen that, when the network
is trained without $L_{1}$ and SSIM loss, it shows more stable performance in
terms of both SSIM and PSNR. If the training losses include $L_{1}$ and SSIM
loss, the highest values of both SSIM and PSNR are achieved when $\mu_{test}$
is close to 0.4. This is due to the fact that the artificially selected
reference images in the LOL-V2 dataset have a mean value of 0.41 in their V
channels. There are very few images’ V channels with a mean brightness above
0.5, which causes SSIM and PSNR drop significantly when the value of
$\mu_{test}$ is higher.

Moreover, in Fig. 9(b), we can see that the network trained with $L_{1}$, SSIM
and $L_{structure}$ loss achieves the highest SSIM. In Fig. 9(a), the network
trained with $L_{1}$, SSIM and $L_{brightness}$ achieved the highest PSNR.
This demonstrates the effectiveness of $L_{structure}$ and $L_{brightness}$ in
improving structure and brightness restoration, respectively.

Table 5: The influence of GFE component and loss functions based on relative
information. During training, the input $\mu_{train}$ value can be a constant
(e.g., $\mu_{train}=0.4$) or obtained through the reference(e.g.,
$\mu_{train}$ equals the mean value of the reference’s V channel in this
table). During testing, the input $\mu_{test}$ value is a constant for all
images in this table ($\mu_{test}=0.4$). Relative losses represents
$L_{color}+L_{brightness}+L_{structure}$

Loss functions | GFE | $\mu_{test}=0.4$ | LOL-V2
---|---|---|---
$L_{1}$+SSIM | Relative losses | component | $\mu_{train}=0.4$ |  $\mu_{train}$ from reference | PSNR$\uparrow$ | SSIM$\uparrow$
✓ |  |  |  |  | 18.32 | 0.80
✓ | ✓ |  |  |  | 19.05 | 0.82
✓ |  | ✓ | ✓ |  | 20.59 | 0.83
✓ |  | ✓ |  | ✓ | 22.62 | 0.84
✓ | ✓ | ✓ |  | ✓ | 23.50 | 0.86

Contribution of GFE component: In this ablation study, the network trained
with $L_{1}$ and SSIM loss without the GFE component was considered as the
baseline model. The effects of adding the GFE component and losses proposed in
this paper were then compared and studied. The results are presented in Table
5. It should be noted that the input $\mu_{test}$ value is constant for all
images during testing in this table.

Table 5 demonstrates that when we add either the other proposed loss functions
or the GFE component to the baseline model, both PSNR and SSIM values show
improvement. This provides strong evidence for the effectiveness of the GFE
component and the loss functions designed with relative information. The GFE
component can capture global brightness information and integrate it into the
enhancement process with few parameters, leading to a significant improvement
in PSNR by 2.27 dB and SSIM by 0.03 (PSNR: $18.32\rightarrow 20.59$, SSIM:
$0.80\rightarrow 0.83$), even with fixed $\mu_{test}$ and $\mu_{train}$ values
during testing and training.

Furthermore, we observed that when the $\mu_{train}$ value is calculated from
the reference images during training, the improvement in PSNR and SSIM values
is even more significant (e.g., PSNR: $18.32\rightarrow 22.63$, SSIM:
$0.80\rightarrow 0.84$). This finding highlights the challenge posed by the
one-to-many problem in learning how to remove noise and retain structural
information in low-light image enhancement. Therefore, the GFE component,
which is a simple and efficient method for connecting the input and output
images, can greatly improve the enhancement results by facilitating the
learning process.

Table 6: The influence of combining the $L_{brightness}$ and $L_{structure}$
with RetinexNet on LOL-V1 dataset. In the original paper(Wei ., 2018),
RetienxNet was trained with LOL-V1 dataset, and the authors used BM3D to
denoise the reflectance image.

Original loss | BM3D | $L_{brightness}\&L_{structure}$ | PSNR$\uparrow$ | SSIM$\uparrow$ | CIEDE2000$\downarrow$
---|---|---|---|---|---
✓ |  |  | 16.79 | 0.42 | 15.89
✓ | ✓ |  | 17.86 | 0.78 | 13.76
✓ |  | ✓ | 18.87 | 0.79 | 12.01

###  4.4 Combined With Other Networks

The proposed $L_{brightness}$ and $L_{structure}$ loss functions can also be
combined with other supervised image enhancement methods to improve their
performance with fewer operations or parameters . For example, BM3D or
additional sub-network is adopted to denoise on the reflectance image in
Retinex based low-light image enhancement methods(e.g., RetinexNet (Wei .,
2018), KIND (Y. Zhang ., 2019), and KIND++(C. Li ., 2021)). However, if we add
the proposed two relative loss functions into the training of the network,
their performace can be imporved without the additional part. Table 6, 7 and
Fig. 10, 11 show the examples of combining $L_{brightness}$ and
$L_{structure}$ with RetinexNet and KIND.

RetinexNet was trained with LOL-V1 dataset in the original paper (Wei .,
2018), and BM3D was used for denoising reflectance images. By adding the two
proposed relative loss functions to the training of RetinexNet, the network
achieves better PSNR, SSIM, and CIEDE2000 scores than the original RetinexNet
and RetinexNet combined with BM3D, as Table 6 shows. Also, as seen in Fig. 10,
RetinexNet with $L_{brightness}$ and $L_{structure}$ loss functions can
significantly reduce noise in the enhanced image (Fig. 10(b) and (d)).
Compared with the BM3D method (Fig. 10(c)), proposed relative loss functions
can help preserve more details and restore the color (Fig. 10(d)).

Figure 10: The visual effect of combining the proposed loss functions with
RetinexNet. (a) The input low-light images. (b) Results of RetinexNet without
BM3D. (c) Results of RetinexNet with BM3D. (d) Results of RetinexNet without
BM3D and with $L_{brightness}$ and $L_{structure}$ in the training loss
function. (e) Reference images. In the original paper (Wei ., 2018),
RetinexNet was trained with LOL-V1 dataset and BM3D was used to denoise on the
reflectance image. (Best viewed on high-resolution displays with zoom-in.)

KIND consists of three sub-networks: DecomNet, RestorNet, and AdjustNet. By
adding the proposed relative loss functions to the training of DecomNet,
DecomNet achieved better results than the entire KIND method, as shown in
Table 7. At that time, the number of parameters can be reduced by nearly
$95\%$.

Table 7: The influence of combining the $L_{brightness}$ and $L_{structure}$
with KIND on LOL-V1 dataset. In the original paper(Y. Zhang ., 2019), KIND was
trained with LOL-V1 dataset. KIND has three sub-networks, which are the
Decomposition Network, the Restoration Network, and the Illumination
Adjustment Network. They are abbreviated as DecomNet, RestorNet, and AdjustNet
in this table.

DecomNet | RestorNet$\&$AdjustNet | $L_{brightness}\&L_{structure}$ | PSNR$\uparrow$ | SSIM$\uparrow$ | CIEDE2000$\downarrow$ | Params(M)$\downarrow$
---|---|---|---|---|---|---
✓ |  |  | 15.68 | 0.50 | 18.73 | 0.43
✓ | ✓ |  | 17.65 | 0.78 | 12.49 | 8.21
✓ |  | ✓ | 18.94 | 0.80 | 11.93 | 0.43

Figure 11 show some images of combining the relative loss functions with
DecomNet of KIND. It can be seen that, the relative loss functions have
positive impact on noise reduction, color correction, and detail preservation.
Thus, we can obtain comparable or superior results using a simpler network
structure with the two proposed relative loss functions.

Figure 11: The visual effect of combining the loss function with DecomNet of
KIND. KIND has three sub-networks, which are the Decomposition Network, the
Restoration Network, and the Illumination Adjustment Network. They are
abbreviated as DecomNet, RestorNet, and AdjustNet in this table. (a) The input
low-light images. (b) Results of DecomNet in KIND. (c) KIND. (d) DecomNet in
KIND with $L_{brightness}$ and $L_{structure}$ in the original loss function.
(Best viewed on high-resolution displays with zoom-in.)

##  5 Conclusion

In this paper, we have demonstrated that by using efficient global feature
extraction and the proposed relative loss functions, a simple network
structure can be employed to achieve image enhancement that is comparable to,
or even better than, the current state-of-the-art (SOTA) methods with much
less running time. Moreover, the Global Feature Extraction component and loss
functions can be combined with other low-light image enhancement techniques to
enhance objective evaluation indicators such as PSNR and SSIM. The
experimental results show the effectiveness and advantages of our method for
low-light image enhancement. However, our approach still has some limitations,
such as the dependence of the final enhancement result on the desired
brightness parameter $\mu_{test}$ and the requirement for paired data during
training. To address the first issue, parameters can be automatically
selected, as demonstrated in our previous work (Q. Fu ., 2020), or the
contrast of the enhanced image can be further adjusted through GAMMA
Correction or other local tone mapping techniques (Zeng ., 2020). In future
research, we aim to improve the robustness of the proposed method and explore
unsupervised approaches for network training.

Acknowledgments The authors would like to thank for National Natural Science
Foundation of China (No. 62027283 and 61775048), Aeronautical Science
Foundation of China(No.2022Z071077002) and Shenzhen Fundamental Research
Program (No. JCYJ2020109150808037) Funded.

## Declarations

  * •

The authors have no competing interests to declare that are relevant to the
content of this article.

  * •

The code is available at https://github.com/hitzhangyu/FLW-Net

  * •

The data used in the paper is sourced from publicly published papers or
publicly available websites. However, if there are reasonable justifications,
it is also possible to request the data from the corresponding authors.

  * •

Y.Zhang designed the workflow, and wrote the manuscript. J.Wu., Y.Wang.,
Y.Li., and R.Fu. provided some ideas and solved some problems in the work, and
contributed to the manuscript. Y.Xu. and Y.Guo provide some ideas and
contributed to the manuscript. X.Xiao, and C.Wang. supervised the work and
contributed to the manuscript.

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