# PriorNet: A Novel Lightweight Network with Multidimensional Interactive
Attention for Efficient Image Dehazing

Yutong Chen  University of Science and Technology of ChinaHefeiAnhuiChina
<EMAIL_ADDRESS>,  Zhang Wen  Ocean University of
ChinaQingdaoShandongChina<EMAIL_ADDRESS>,  Chao Wang  University of
Science and Technology of ChinaHefeiAnhuiChina<EMAIL_ADDRESS>,  Lei Gong
University of Science and Technology of ChinaHefeiAnhuiChina
<EMAIL_ADDRESS>and  Zhongchao Yi  University of Science and
Technology of ChinaHefeiAnhuiChina<EMAIL_ADDRESS>
###### Abstract.

Hazy images degrade visual quality, and dehazing is a crucial prerequisite for
subsequent processing tasks. Most current dehazing methods rely on neural
networks and face challenges such as high computational parameter pressure and
weak generalization capabilities. This paper introduces PriorNet—a novel,
lightweight, and highly applicable dehazing network designed to significantly
improve the clarity and visual quality of hazy images while avoiding excessive
detail extraction issues. The core of PriorNet is the original Multi-
Dimensional Interactive Attention (MIA) mechanism, which effectively captures
a wide range of haze characteristics, substantially reducing the computational
load and generalization difficulties associated with complex systems. By
utilizing a uniform convolutional kernel size and incorporating skip
connections, we have streamlined the feature extraction process. Simplifying
the number of layers and architecture not only enhances dehazing efficiency
but also facilitates easier deployment on edge devices. Extensive testing
across multiple datasets has demonstrated PriorNet’s exceptional performance
in dehazing and clarity restoration, maintaining image detail and color
fidelity in single-image dehazing tasks. Notably, with a model size of just
18Kb, PriorNet showcases superior dehazing generalization capabilities
compared to other methods. Our research makes a significant contribution to
advancing image dehazing technology, providing new perspectives and tools for
the field and related domains, particularly emphasizing the importance of
improving universality and deployability.

Image Dehazing, Lightweight Neural Network, Generalization Capability,
Multidimensional Interactive Attention (MIA)

††ccs: Computing methodologies Computer vision tasks††ccs: Computing
methodologies Computer vision problems††ccs: Computing methodologies Computer
vision representations

##  1\. Introduction

Images captured in foggy or hazy conditions often exhibit reduced visual
quality, characterized by lower contrast and color distortion (4587643, ).
This degradation not only negatively impacts the visual experience, but also
poses significant challenges for computer vision applications, such as image
classification and object detection, which largely rely on datasets composed
of clear images (ren2016single, ), (blasinski2018optimizing, ). As a result,
images obtained in hazy conditions can adversely affect the performance of
advanced visual tasks. To ensure these tasks are completed effectively, it is
imperative that input images are either free of haze or minimally impacted by
it. In recent years, the field of image dehazing, which focuses on restoring
clear scenes from hazy images, has received widespread attention from both the
academic and industrial sectors.

Initial research in dehazing primarily relied on atmospheric scattering
models, which offer a simplified approximation of fog effects as shown in the
equation (mccartney1976optics, ), (meng2013efficient, ),
(narasimhan2000chromatic, ):

(1) $I(z)=J(z)t(z)+A(1-t(z))$

In this model,I(z) represents the observed hazy image, A is the global
atmospheric light, t(z) is the medium transmission map, and J(z) denotes the
haze-free image. Early studies highlighted the practical applicability of this
model, with the Dark Channel Prior (DCP) method (he2010single, ) emerging as a
notably effective solution in real-world conditions due to its computational
efficiency. However, methods based on priors may encounter challenges due to
inaccurate estimations of the transmission map, often resulting from
violations of prior assumptions in practical scenarios, potentially limiting
their effectiveness. This can lead to color distortion or the presence of
halos and light patches around edges, impacting the progress of subsequent
tasks.

Recent advancements in dehazing research have unequivocally affirmed the
superior efficacy of deep neural networks in image dehazing techniques,
encompassing both CNN (cai2016dehazenet, ), (li2017aod, ), (li2020deep, ),
(zhang2018densely, ) and Transformer (qiu2023mb, ), (song2023vision, ),
(liu2023visual, ) architectures. With the increasing depth of these networks
and the integration of various attention mechanisms throughout the dehazing
process, there has been a notable enhancement in network performance
(lu2023mixdehazenet, ), (chen2024dea, ). However, this enhancement comes at
the cost of escalated algorithmic complexity. This complexity introduces two
primary challenges: an exponential increase in the parameter count, elevating
the costs associated with training and inference, and a decline in the
generalization capability. While these sophisticated algorithms excel in
specific datasets, their robustness diminishes when applied to alternative
datasets or under the fluctuating conditions of the real world. This situation
highlights the pressing need to explore strategies that maintain computational
efficiency while improving the reliability and broad applicability of dehazing
algorithms.

To address the challenges in the field of dehazing, we introduce a novel,
lightweight, and highly generalizing dehazing network (named PriorNet). This
approach harnesses neural network techniques to extract fundamental features
from actual images, followed by the application of the atmospheric scattering
model for image restoration. In the extraction phase, the method leverages the
nonlinear abstraction capabilities of neural networks to extract haze
characteristics that are challenging to quantify or derive. For restoration,
it emphasizes the application of a physical model,namely AMS
(narasimhan2003contrast, ), to achieve accurate dehazing. DCP highlights the
extremely low intensity in at least one RGB channel of certain pixels, while
also observing that haze distribution within images exhibits regional
characteristics - neither uniformly spread across the entire image nor
presenting pixel-level variances. Thus, there arises an urgent need for a new
type of attention mechanism that is neither as coarse as channel attention nor
as overly detailed as spatial attention. In response, we propose the
Multidimensional Interactive Attention (MIA), designed to capture the broad
haze features across different regions, avoiding the high computational strain
and reduced generalizability associated with complex attention mechanisms,
thereby achieving simplicity and efficiency. Moreover, by utilizing a shallow
network architecture and uniform convolutional kernels, our network focuses on
extracting the most crucial information, preventing excessive detail
extraction for more effective dehazing outcomes.Furthermore, in the feature
extraction phase, our network deviates from the traditional approach of
utilizing various convolutional kernel sizes. Instead, it opts for a single
kernel size, coupled with the use of skip connections, to capture a more
comprehensive array of physical information. By constraining our network to 5
convolutional layers and 3 concatenation layers, we not only ensure the
thoroughness of information capture at a consistent scale, avoiding the
extraction of excessive detail, but also significantly reduce the total
parameter count of the network. This streamlined architecture facilitates
easier deployment on edge devices, optimizing both efficiency and
practicality.During the restoration phase, operations are carried out on a
per-pixel basis, details of which will not be elaborated further here.

Our contributions in advancing image dehazing technology focus on three
primary innovations:

  * •

Innovative Network Design (PriorNet): A novel, lightweight dehazing network
distinguished by its remarkable generalization capabilities. PriorNet is
engineered to efficiently process hazy images, enhancing clarity and visual
quality without the need for excessive detail extraction.

  * •

Multidimensional Interactive Attention (MIA):  An innovative attention
mechanism tailored to efficiently capture widespread haze features without the
computational burden and generalization issues of complex systems, steering
towards a more effective dehazing process.

  * •

Optimized Feature Extraction and Restoration: By adopting a uniform
convolutional kernel size and utilizing skip connections, we streamline the
feature extraction process. Our network, with its reduced layer count and
simplified architecture, not only enhances the dehazing efficiency but also
supports easier deployment on edge devices.

##  2\. RELATED WORK

###  2.1. Attention Mechanism

In deep learning, the attention mechanism has emerged as a pivotal technique
(bahdanau2014neural, ), (dosovitskiy2020image, ), acclaimed for its adeptness
in heightening the model’s focus on pivotal elements within the input data
(liu2019griddehazenet, ), (wang2019aagan, ), (jiang2021haze, ). Self-attention
mechanisms elevate model performance by pinpointing long-distance interactions
among inputs, thereby capturing nuances often missed by conventional
approaches (vaswani2017attention, ). Channel attention scrutinizes the
dynamics of feature activations across channels (hu2018squeeze, ),
spotlighting the relational importance of different features, whereas spatial
attention assesses the criticality of information’s spatial layout
(zhu2019empirical, ), optimizing the model’s perceptual field. The advent of
numerous derivatives of these core mechanisms has further broadened the
spectrum of attention module designs, significantly enhancing model
interpretability and adaptability in processing complex datasets.

Notwithstanding the apparent benefits of attention mechanisms, they
unavoidably introduce a significant number of parameters and computational
overheads. Furthermore, in the endeavor to highlight essential information,
there is a potential for models to capture an overabundance of redundant
information, potentially leading to overfitting or a decline in performance in
real-world applications.

To tackle these challenges, we draw inspiration from the domains of physical
models and mathematical statistics, merging channel and spatial attention
mechanisms to innovatively propose the Multidimensional Interactive Attention
(MIA). MIA unites the strengths of traditional channel and spatial attention
mechanisms, effectively extracting fundamental haze features across different
image regions from the input data. With its simplified structure, MIA not only
alleviates computational load and training costs but also avoids the excessive
extraction of information, focusing instead on capturing key details.

###  2.2. Single Image Dehazing

Initial studies in image dehazing were predominantly based on mathematical
statistics and physical methodologies, frequently utilizing atmospheric
scattering models or leveraging specific handcrafted priors (berman2016non, ),
(chen2016robust, ). Although these methods are grounded in solid theoretical
principles, their real-world applicability often encounters limitations due to
the precision of assumed prior conditions, resulting in less-than-ideal
dehazing outcomes in complex environmental situations. The gap between the
theoretical environmental assumptions and the realities of actual conditions
can markedly affect the effectiveness of dehazing techniques.

With the advancement of deep learning technologies, current research
(qin2020ffa, ), (lu2023mixdehazenet, ), (wang2024image, ) has primarily
shifted towards data-driven approaches, especially those employing
Convolutional Neural Networks (CNNs) or Transformer architectures to estimate
atmospheric lighting and transmission maps. The incorporation of numerous
attention mechanisms has significantly enhanced model performance. These
methods construct dehazing models by learning from vast datasets, effectively
improving the accuracy of dehazing. However, an increase in model complexity
also means a rise in the number of parameters and computational load, which
often affects the generalization ability across different datasets and in
real-world application scenarios.

In response to the limitations inherent in existing dehazing methods, we
introduce an innovative dehazing network design. Grounded in the atmospheric
scattering model, our approach diverges from traditional CNN methodologies in
feature extraction. Our model incorporates a novel attention mechanism and
abstracts real-world conditions through a shallow network architecture,
employing single-size convolutional kernels and skip connections, with a
heightened focus on the application of physical models and mathematical
principles. Consequently, our network significantly enhances adaptability and
resilience to changes in real-world environments, while dramatically reducing
the number of parameters and computational demands.

Figure 1. Architecture of PriorNet

##  3\. Methods

###  3.1. Physics Model

In environments impacted by haze, image quality is significantly compromised,
presenting challenges at both global and local levels. Assuming a uniform
distribution of haze within the atmosphere allows for an initial understanding
of the overall haze density within images. However, the degradation of image
quality is not solely influenced by this global haze density but is also
affected by variations in lighting conditions and the distance between objects
and the camera. This necessitates the segmentation of the dehazing problem
into global and local components for a more effective resolution.

The vast majority of dehazing research, ranging from early statistical methods
to contemporary deep neural network algorithms, is grounded on the atmospheric
scattering model. Building on this model, namely equation 1, the image
restoration process can be reformulated as (li2017aod, ):

(2) $J(x)=K(x)\cdot I(x)-K(x)+b$

where

(3) $\
K(x)=\frac{1}{t(x)}\cdot\left(\frac{I(x)-A}{I(x)-1}\right)+\frac{(A-b)}{I(x)-1}$

Here, $K(x)$ acts as a scaling factor adjusting the intensity of the observed
image pixels, and $b$ is a bias term introduced to mitigate potential errors.
The scaling factor $K(x)$ accounts for the attenuation of light caused by the
haze, and the bias $b$ addresses any ambient light potentially skewing the
intensity levels.

In traditional image dehazing methods, the restoration process heavily relies
on mathematical and statistical approaches to estimate atmospheric light $A$
and transmission $t(x)$ separately before proceeding to image recovery. For
instance, the Dark Channel Prior (DCP) algorithm initially calculates the dark
channel image, uses it to estimate atmospheric light $A$, and then combines
the dark channel image with the estimated atmospheric light to deduce the
transmission $t(x)$. Finally, it utilizes the atmospheric scattering model
(AMS) to recover the haze-free image. In contrast, modern methods based on
deep learning adopt a more straightforward approach by directly extracting the
scaling factor $K(x)$, instead of separately determining the transmission map
$t(x)$, atmospheric light $A$, and bias $b$. This approach not only simplifies
the processing steps but also leverages the neural network’s strong capability
in fitting nonlinear problems, effectively overcoming the limitations in
flexibility and adaptability of traditional methods. Thus, it allows for a
more accurate restoration of the original haze-free image $J(x)$.

###  3.2. Network Design

Building upon our previous discussion, we segregate the dehazing challenge
into two principal categories: overarching global concerns and nuanced local
disparities. To adeptly address these divisions, we present PriorNet, a
innovative and ultra-lightweight network framework specifically engineered to
tackle the complexities of the dehazing process. Perfectly aligning with the
forefront of advancements in deep learning for dehazing, PriorNet encompasses
two essential components: a sophisticated deep learning estimation module for
$K(x)$ analysis and an image restoration module that employs fundamental
operations for the reconstruction of dehazed images. This restoration module
relies heavily on a methodical direct estimation of $K(x)$ for reconstructing
images on a pixel-by-pixel basis, a methodology thoroughly vetted in prior
studies. Therefore, we opt not to reiterate on this process. The essence of
our network’s design resides in the $K(x)$ estimation module, which cleverly
merges a convolutional extraction pathway with a multidimensional interactive
attention (MIA) framework, as depicted in Figure 1. This estimation module
inputs hazy images to directly output feature maps. In this section, we aim to
meticulously delve into the specifics of these two foundational elements.

###  3.3. Multidimensional Interactive Attention

In response to the inherent properties of haze, we have endeavored to
integrate modules adept at gleaning both overarching and nuanced details. This
initiative led to the development of the Multidimensional Interactive
Attention (MIA). MIA leverages a traditional channel attention mechanism to
discern global fog characteristics, while it harnesses a uniquely devised
spatial attention mechanism to accurately extract information from pivotal
regions within the image.

The channel attention mechanism operates according to the principle outlined
in Equation 4. This mechanism employs a combination of average pooling and max
pooling to process the feature map $F$, subsequently integrating the outcomes
through a multi-layer perceptron (MLP) with shared weights. The MLP consists
of two weight matrices, $W_{0}$ and $W_{1}$, and incorporates a ReLU
activation function post the first weight layer. The final channel attention
map, $M_{c}(F)$, is generated by applying the sigmoid function $\sigma$ to the
aggregated MLP outputs, offering a refined method to dynamically emphasize
informative features.

(4)
$M_{c}(F)=\sigma\left(W_{1}\left(W_{0}\left(\text{AvgPool}(F)\right)+W_{0}\left(\text{MaxPool}(F)\right)\right)\right)$

Here, $\sigma$ represents the sigmoid function, indicating a non-linear
transformation applied to the MLP outputs. The matrix
$W_{0}\in\mathbb{R}^{r\times c}$ acts as the initial transformation layer
within the MLP, followed by $W_{1}\in\mathbb{R}^{c\times c/r}$, which further
refines the attention mechanism’s output.

Figure 2. Architecture of the MIA

We have engineered an advanced spatial attention mechanism specifically
designed to identify local features, structured in three primary sections, as
illustrated in Figure 2.

The initial phase is the local spatial attention module, which employs a
sliding window technique to partition the hazy image, thereby isolating
significant local features. A fully connected layer is then employed to
bolster the interchange of channel information among these features. Once this
process is complete, the feature vectors are expanded to their original
dimensions.

(5)
$F_{local}\left(x_{hazy}\right)=F_{ex}\cdot\left(F_{ReLU}\cdot\left(F_{MLP}\left(F_{sw}\left(x_{hazy}\right)\right)\right)\right)$

In Equation 5, The expansion operator, denoted as $F_{ex}$, ensures that
features are resized back to their original dimensions. $F_{ReLU}$ signifies
the ReLU activation function, $F_{MLP}$ refers to a fully connected layer, and
$F_{sw}$ is the sliding window average pool operator, characterized by a
stride of 4 and a window size of 8x8.

Subsequently, our spatial cross-attention framework is divided into two parts:
initially, feature enhancement is achieved through a fully connected layer;
following this, channel and spatial features are derived using average pooling
and convolution operations. These features are then combined through a
reshaping and cross-multiplication strategy, effectively merging spatial and
channel data. The local spatial features and these cross features are then
integrated through a multiplicative fusion.

(6)
$F_{SP}\left(x\right)=F_{SG}\left[\sigma_{3}\left(F_{SM}\left(\sigma_{1}\left(F_{GP}\left(W_{q}\left(x\right)\right)\right)\right)*\sigma_{2}\left(W_{2}\left(x\right)\right)\right)\right]$

In this context, $F_{sp}$ $\in$ $\mathbb{R}^{1\times H\times W}$, with
$F_{GP}$ signifying the global pooling layer, as delineated in Equation 7.

(7)
$F_{GP}\left(x\right)=\frac{1}{H*W}\sum_{i=1}^{H}{\sum_{j=1}^{W}{x}\left(:,i,j\right)}$

The operation of the softmax function is represented by $F_{SM}(\cdot)$,
detailed in Equation 8, while the sigmoid function is encapsulated by
$F_{SG}(X_{pro}(\cdot))$, as expounded in Equation 9.

(8)
$F_{SM}\left(x_{pro}\left(x_{i},y_{i},c_{i}\right)\right)=\frac{e^{x_{pro}\left(x_{i},y_{i},c_{i}\right)}}{\sum_{x_{j}\epsilon\left(0,H\right)}{\sum_{y_{j}\epsilon\left(0,H\right)}{\sum_{z_{j}\epsilon\left(0,H\right)}{e^{x_{pro}\left(x_{j},y_{j},c_{j}\right)}}}}}$

(9)
$F_{SG}\left(x_{pro}\left(x_{i},y_{i},c_{i}\right)\right)=\frac{1}{1+e^{-x_{pro}\left(x_{i},y_{i},c_{i}\right)}}$

The ’$\times$’ symbolizes the matrix product operator, while $W_{q}$ and
$W_{v}$ are tensor reshape operators. $\sigma 1$, $\sigma 2$, $\sigma 3$ are
additional tensor reshape operators.

The finale of this process involves the amalgamation of these two feature
sets. The local features serve to enhance the cross features, shown as
equation 10.

(10)
$F_{atten}\left(x_{hazy}\right)=F_{SG}\left(F_{cocal}\left(x_{hazy}\right)\odot
F_{sp}\left(x_{hazy}\right)\right)$

Ultimately, all the extracted and combined features are brought together
through a convolutional procedure, resulting in the production of the
ultimate, polished image.

Figure 3. Architecture of Convolutional Feature Extraction Module

###  3.4. Convolutional Feature Extraction Module

Leveraging the structural insights of AOD-Net (li2017aod, ) and the profound
analytical rigor of statistical methods exemplified by DCP (he2010single, ),
our approach is grounded in the robust principles of mathematics and physics,
aiming to demystify the complexities inherent in haze characterization.
Consequently, we’ve streamlined our convolutional feature extraction
architecture, as illustrated in Figure 3, which consists of five convolutional
layers paired with three Concat operations, ensuring a thorough extraction of
features. Diverging from traditional pixel-centric methods, we posit that haze
predominantly exhibits a regional distribution. This pivotal realization
steered us towards standardizing our convolutional kernel size, thereby
sidestepping the need for a diverse arsenal of convolutional operations. After
meticulous evaluation, we adopted a 5x5 kernel size, identified as the ideal
choice for enhancing network performance due to its well-balanced receptive
field.

Furthermore, the ”concat1” layer skillfully merges features from ”conv1” and
”conv2”, while ”concat2” and ”concat3” seamlessly integrate features from
subsequent convolutional layers, with each layer’s contribution distinctly
highlighted in different colors within the figure 3for enhanced visual
clarity. This multi-scale feature fusion methodology is key to mining pivotal
information from across the entire image, substantially elevating the
network’s efficiency in discerning and mitigating haze. These deliberate
design decisions, including an optimized network architecture with a reduced
count of layers and parameters and a strategic choice to limit convolutional
kernel sizes, culminate in PriorNet. This platform embodies a sophisticated
yet highly effective dehazing solution, deeply informed by an understanding of
the regional nature of haze, setting a new standard in the field of image
dehazing.

###  3.5. Loss Function

In our model, we utilize the Mean Squared Error (MSE) as the loss function to
quantify the discrepancies between the original and the output images, defined
as:

(11)
$Loss_{mse}=\frac{1}{C*H*W}\sum_{x_{i}\in\left[0,H\right]}\sum_{y_{i}\in\left[0,W\right]}\sum_{c_{i}\in\left[0,C\right]}\\\
\left[x_{gt}\left(x_{i},y_{i},c_{i}\right)-x_{pro}\left(x_{i},y_{i},c_{i}\right)\right]^{2}$

where $X_{gt}$ represents the clean, haze-free image, $X_{pro}$ is the
network’s output, $H$ is the height of the image, $W$ is the width, and $C$
denotes the channels.

Additionally, to enhance the human perceptual quality of the processed images,
we integrate a perceptual loss function, utilizing a pre-trained Vgg16 network
as the perceptual evaluator (qu2020crack, ):

(12)
$Loss_{perception}=\frac{1}{N}\sum_{i=1}^{N}{\left(F_{Vgg16}\left(x_{gti}\right)-F_{Vgg16}\left(x_{pro\
i}\right)\right)^{2}}$

with $N$ being the batch size and $F_{Vgg16}$ the Vgg16 network equipped with
pre-trained weights.

To align the processed images closely with their originals, we adopt a
coefficient $beta=0.1$ to temper the perceptual loss’s effect:

(13) $Loss=Loss_{mse}+\beta\cdot Loss_{perception}$

This formulation not only aims at minimizing the direct errors between images
but also at improving their realism and visual appeal to the human eye, while
preserving image detail and quality.

##  4\. EXPERIMENTS

In this section, we will firstly describe the experimental setup. After that,
the results of the experiments and an ablation study of PriorNet will be
illustrated.

###  4.1. Experiment Settings

#### Datasets.

To precisely assess the generalization capacity of various dehazing models,
our research utilized two distinct datasets: ”Haze4k” (liu2021synthetic, ) and
”Hazy_NYU_Depth-V2” (li2017aod, ). For ease of reference in further
discussions, the latter is abbreviated as ”Hazy_NYU
_DepthV2”, which consists of hazy images from the NYU Depth V2 dataset and has
been previously utilized for testing within the AOD-Net framework. It is
critical to mention that the designations adopted in this study are solely for
the convenience of expression and do not correspond to their official titles.
The choice of the ”Haze4k” dataset is justified by its prevalent use in the
training of dehazing algorithms, whereas the ”Hazy_NYU_DepthV2”, derived from
the NYU Depth V2 dataset, facilitates a more extensive spectrum of
experimental automation by supporting tasks in both dehazing and recognition
domains.

#### Implementation Details.

Our methodology employs a dual-source approach for testing models.
Specifically, we utilize models in their original form if they were previously
trained on the ”Haze4K” dataset, adhering to the configurations established by
their creators. For models that lack prior training on ”Haze4K,” we undertake
a rigorous retraining process on this dataset to ensure they are well-adapted
for evaluation. This enables us to establish the most effective parameters for
these models, tailoring their performance to our assessment criteria. All
models are evaluated against the ”Hazy_NYU_DepthV2” test set to ensure a fair
and accurate comparison of their real-world effectiveness. This strategy
allows us to assess models from both sources under consistent conditions,
offering insights into their generalization capabilities and adaptability
across different scenarios.

#### Comparison Methods and Evaluation Metrics.

In our quantitative analysis of various dehazing methods, we began by
comparing image metrics obtained from training on one dataset and testing on
another, to rigorously evaluate each model’s adaptability and effectiveness
beyond its initial training environment. Our study encompasses a broad
spectrum of dehazing techniques, notably the Dark Channel Prior (DCP)
(he2010single, ) method, famed for its reliance on statistical principles and
independence from training data. It should be noted that since the Dark
Channel Prior method yields results directly without the need for training, we
directly applied DCP to the test dataset. The intentional inclusion of DCP as
a benchmark was to gauge the performance of our innovative solutions against
existing advanced neural network models, such as MixDehazeNet. Utilizing
quantitative metrics like Peak Signal-to-Noise Ratio (PSNR) and Structural
Similarity Index (SSIM) (wang2004image, ), we aimed to assess the success rate
of these dehazing techniques, with a particular focus on their generalization
capabilities across various scenarios. Additionally, we compared the parameter
sizes of different models. Although the size of the model parameter set was
considered a secondary factor in our analysis, our primary focus was on
elucidating the operational efficiency of each dehazing strategy. Lastly,
given dehazing’s significance as a crucial preprocessing step for subsequent
advanced image tasks, we further tested the effectiveness of different models
in actual applications by using the dehazed images for object recognition
tasks, thereby evaluating their real-world impact on advanced imaging tasks.

###  4.2. Quantitative Analysis of Generalization Across Datasets

In our detailed quantitative evaluation, we focus on assessing the
generalization capabilities of a broad spectrum of dehazing methods. This
involved training models on a specific dataset and then testing them on a
distinct one, meticulously examining each model’s ability to perform robustly
beyond its original training environment. Such an approach enabled us to
thoroughly evaluate the adaptability and effectiveness of each method,
extending well beyond their initial training parameters. Central to our study
was the Dark Channel Prior (DCP) method, celebrated for its reliance on
statistical foundations and its unique characteristic of not requiring
training data. Through the application of quantitative metrics like Peak
Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM), we aimed
to systematically measure the dehazing efficacy of these techniques, with a
keen focus on their capacity to adapt across varied conditions. Additionally,
we considered the parameter sizes of the models as a secondary yet insightful
aspect of our evaluation. Given the pivotal importance of dehazing in
preparing images for advanced processing tasks, we further investigated the
real-world utility of these models through their application in object
recognition tasks, thereby gauging their substantive influence on complex
imaging challenges.

#### Evaluation on Haze4K

In accordance with the experimental setup described earlier, we initially
trained our model using the Hazy_NYU_DepthV2 dataset and conducted testing on
the Haze4K dataset, as outlined in Table 1. It’s noteworthy that PriorNet
exhibited remarkable performance in these tests, boasting a PSNR of 17.2756
and an SSIM of 0.8329. These results highlight its exceptional ability to
generalize and efficiently tackle diverse dehazing tasks and environmental
conditions. In contrast, DCP only achieved modest results with a PSNR of
14.0990 and an SSIM of 0.7588. This disparity underscores the limitations of
DCP, which relies heavily on statistical principles and preset haze estimation
conditions, leading to reduced performance when real-world conditions deviate
from these assumptions. In comparison to the lightweight model AODNet,
PriorNet displayed significantly superior performance. While larger models
such as DEA Net and MixDehazeNet showed promise in dehazing, their
generalization capabilities were comparatively lacking.

Table 1. Results on Haze4K. Method |  Venue | Metrics
---|---|---
|  | PSNR | SSIM
DCP (he2010single, ) |  TPAMI’10 | $14.0990$ | $0.7588$
DEA-Net (chen2024dea, ) |  TIP’24 | $12.9566$ | $0.7326$
DehazeFormer (song2023vision, ) |  TIP’23 | $10.8677$ | $0.6355$
DFF-Net (wang2024image, ) |  - | $11.8655$ | $0.7387$
AOD-Net (li2017aod, ) |  ICCV’17 | $15.1254$ | $0.7525$
MixDehazeNet (lu2023mixdehazenet, ) |  IJCNN’24 | $13.0012$ | $0.7331$
PriorNet (Ours) |  - | 17.2756 | 0.8329

#### Evaluation on Hazy_NYU_DepthV2

To ensure a comprehensive evaluation of the generalization abilities of
various dehazing methods, we inverted the roles of the test and training
datasets—training on the Haze4k dataset and testing on Hazy_NYU_
DepthV2. The detailed results of these evaluations are meticulously recorded
in Table 2. Our observations reveal that PriorNet demonstrates remarkable
adaptability and performance on unfamiliar datasets, achieving a Peak Signal-
to-Noise Ratio (PSNR) of 17.1608 and a Structural Similarity Index (SSIM) of
0.7660. These achievements firmly establish PriorNet as a leading contender
among all the neural network-based methods we evaluated. Notably, when
compared to AOD-Net, which attained PSNR of 14.5292 and SSIM of 0.7136,
PriorNet showcases relatively superior generalization capabilities despite
similar parameter counts. However, the performance of other neural network
models falls short in comparison. It’s noteworthy that the Dark Channel Prior
(DCP) method outperforms all models, achieving an impressive PSNR of 18.6280
and SSIM of 0.7819, primarily because the Hazy_NYU_DepthV2 dataset adheres to
prior conditions.

Table 2. Results on Hazy_NYU_DepthV2. Method |  Venue | Metrics
---|---|---
|  | PSNR | SSIM
DCP |  TPAMI’10 | $18.6280$ | $0.7819$
DEA-Net |  TIP’24 | $14.8864$ | $0.7233$
DehazeFormer |  TIP’23 | $9.3744$ | $0.5908$
DFF-Net |  - | $11.4134$ | $0.7302$
AOD-Net |  ICCV’17 | $14.5292$ | $0.7136$
MixDehazeNet |  IJCNN’24 | $13.9572$ | $0.7168$
PriorNet (Ours) |  - | $17.1680$ | $0.7660$

###  4.3. Comparative Analysis of Model Parameter Sizes

The data presented in Table 3 unequivocally illustrates the substantial
advantage of PriorNet in terms of the number of model parameters. Relative to
extant technologies, the parameter count of most models is at least two orders
of magnitude greater than that of our proposed method. This disparity is even
more pronounced in the realm of multi-task processing, where the current
state-of-the-art model, MixDehazeNet, possesses a parameter volume that
surpasses ours by three orders of magnitude. This marked reduction in
parameter count not only signifies considerable savings in computational
resources and storage capacity but also facilitates the deployment on edge
devices. It is particularly noteworthy that despite the drastic reduction in
parameter numbers, PriorNet demonstrably outperforms all current models on the
market in terms of generalization performance, a fact that our experimental
results have robustly validated.

Table 3. Model Parameter Sizes of Dehazing Methods Methods | Size (Kb)
---|---
MixDehazeNet | 143387
DEA-Net | 14331
DFF-Net | 68739
DehazeFormer | 5593
AOD-Net | 11
PriorNet (Ours) | 18

###  4.4. Ablation Studies

In the ablation studies we conducted, by sequentially removing key components
from PriorNet, we explored their specific impact on the performance of image
dehazing. We focused on evaluating the effects of removing the
Multidimensional Interactive Attention (MIA) mechanism and employing non-
uniform convolutional kernel sizes. The results, as shown in Table 4,
conclusively highlight the central role of the MIA mechanism in enhancing the
model’s dehazing effectiveness; concurrently, the use of uniform convolutional
kernel sizes and a simplified network architecture collectively contribute to
the model’s efficiency and generalization capabilities. This series of
experiments not only confirms the importance of each element within the design
of PriorNet but also emphasizes their interplay, providing a solid foundation
for efficiently and effectively addressing the problem of image dehazing.

Table 4. Ablation Study Results on PriorNet Method | PSNR | SSIM
---|---|---
Only 3 * 3 | $13.3155$ | $0.6897$
Only 5 * 5 | $14.6674$ | $0.7156$
CA + 5 * 5 | $15.2460$ | $0.7201$
MIA + Multi_coresize | $14.5292$ | $0.7136$
Figure 4. Visual Results of Dehazing Methods.

###  4.5. The Influence of Image Dehazing on Future Vision Tasks

To comprehensively evaluate the quality of images processed by various
dehazing methods, we employed a YOLOv4 (bochkovskiy2020yolov4, ) model trained
on the COCO dataset (lin2014microsoft, ) to identify objects within the
processed images from the Hazy_NYU_DepthV2 dataset. As shown in the table 5,
PriorNet clearly demonstrates the best performance, closely followed by DCP.
However, it’s worth noting that as the image quality improves, the enhancement
in object recognition tasks from each method appears to encounter a
bottleneck.

Table 5. Ablation Study Results on PriorNet Method | Accuracy
---|---
DCP | $0.6612$
MixDehazeNet | $0.5156$
DEA-Net | $0.6122$
DFF-Net | $0.6166$
DehazeFormer | $0.6134$
AOD-Net | $0.6565$
PriorNet (Ours) | $0.6732$

##  5\. Visual Results and Analysis

Figure 4 presents a comparative analysis of the efficacy of various dehazing
techniques, clearly illustrating that aside from DeHazeFormer, the performance
of other methodologies on the Hazy_NYU
_DepthV2 dataset is quite notable. However, a critical observation reveals
that DCP encounters severe color distortion due to its reliance on built-in
prior assumptions, leading to pronounced halos and light patches near object
edges, significantly impeding the accuracy and implementation complexity of
subsequent tasks. Moreover, while DFFNet and AOD-Net have made strides in
reducing haze, they consistently generate images with diminished brightness,
indicating that the haze effects are not fully eradicated. DFFNet shows
overall better results compared to AOD-Net, yet some areas with low luminance
still suffer from inadequate dehazing. On the other hand, DEA-Net and
MixDehazeNet struggle to maintain clarity at the edges or textures of objects,
resulting in noticeable blurring that compromises the sharpness and detail of
the images.In contrast, Priornet distinguishes itself by offering the most
outstanding overall visual experience in dehazing. Our network significantly
showcases its superior performance in processing image details and maintaining
color fidelity, illustrating its exceptional capabilities in enhancing visual
clarity and vibrancy.

##  6\. Conclusion

In this study, we draw upon the principles of mathematical models and merge
them with the potent abstraction capabilities of neural networks to conceive
an innovative attention mechanism. This mechanism integrates channel and
spatial attention strategies, aimed at effectively capturing the coarse
features present in complex real-world scenarios, and is designated as the
Multidimensional Interactive Attention (MIA). Building upon MIA, we further
introduce Priornet—a lightweight dehazing network characterized by its
remarkable generalization ability, demonstrating superior performance in the
task of single-image dehazing.The architecture of Priornet is both simple and
efficient, ensuring high accuracy in dehazing operations while its lightweight
nature facilitates effortless deployment on edge devices. Extensive testing
across various datasets has validated Priornet’s formidable capability in haze
removal and clarity restoration, alongside its exceptional preservation of
image details and color fidelity. Overall, our work not only advances the
field of image dehazing but also offers a new perspective and tool for related
domains, especially in the pursuit of generalization and deployability.

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