Quality-Improved and Property-Preserved Polarimetric Imaging via Complementarily Fusing
Authors: Chu Zhou
Yixing Liu
Chao Xu
Boxin Shi
Venue: NeurIPS 2024 poster (2024)
Keywords: Polarimetric Imaging
Exposure fusion
Deep Learning
Primary area: machine_vision
TL;DR: We propose a polarimetric imaging framework that can produce clean and clear polarized snapshots by complementarily fusing a degraded pair of noisy and blurry ones.

Abstract: Polarimetric imaging is a challenging problem in the field of polarization-based vision, since setting a short exposure time reduces the signal-to-noise ratio, making the degree of polarization (DoP) and the angle of polarization (AoP) severely degenerated, while if setting a relatively long exposure time, the DoP and AoP would tend to be over-smoothed due to the frequently-occurring motion blur. This work proposes a polarimetric imaging framework that can produce clean and clear polarized snapshots by complementarily fusing a degraded pair of noisy and blurry ones. By adopting a neural network-based three-phase fusing scheme with specially-designed modules tailored to each phase, our framework can not only improve the image quality but also preserve the polarization properties. Experimental results show that our framework achieves state-of-the-art performance.

Quality-mmproved and Property-Preserved Polarimetric Imaging via Complementarily Fusing
Chu Zhou Yixing Liu Chao Xu* Boxin Shi2.3*
National Institute of Informatics, Japan
2 State Key Laboratory for Multimedia Information Processing, School of CS, Peking University, China
3 National Engineering Research Center of Visual Technology, School of CS, Peking University, China National Key Laboratory of General Artificial Intelligence, School of IST, Peking University, China zhou chu@ho waw.hhotmaal.cmmm com, (luiginixy@stu. xuchao@cis., shiboxin@)pku. edu.
Abstract
Polarimetric imaging is challenging problem in the field of polarization-base vision, since setting short exposure time reduces the signal-to-noise ratio, making the degree of polarization (DoP) and the angle of polarization (AoP) severely de- generated, while if setting relatively long exposure time, the DoP and AoP would tend to be over-smoothed due to the requently-occurrigg motion blur. This work proposes a polarimetric imaging framework that can produce clean and clear polar- ized snapshots by complementarily fusing degraded pair of noisy and blurry ones. By adopting a neural network-based three-phase fusing scheme with specially- designed modules tailored to each phase, our framework can not only improve the image quality but also preserve the polarization properties. Experimental results show that our framework achieves state-of-the-ee performance.
Introduction
Polarimetric imaging aims to obtain the degree of polarization (DoP) and the angle of polarization (AoP) of the scene provide physical clues for downstream polarization- based vision applications reflection removal [16), shape from polarization (5), dehazing (31), etc.). In practice, the DoP and AoP cannot be captured directly, but are usually calculated from polarized snapshots]] in an indirect manner. However, since polarizer would block part of the light, selecting an appropriate exposure time could challenging, making the captured polarized snapshots often degrade [15] 33 As shown in Fig. [ (left), setting short exposure time would result in a very low signal-to-ma noinois ratio (SNR), making the DoP and AoP severely degenerated; while if setting a relatively long exposure time to increase the SNR, motion blur is more likely to occur, making the DoP and AoP over-smoothed, as shown in Fig. (middle) To deal with the above issues, several methods have been proposed to handle the liw-tight noise [10 23 13 32 these methods can work in a polarization-aware manner (i.e., they explicitly take the preservation of polarization properties into consideration), they usually demonstrate higher performance compared
motion blur [33 in the polarized images. Since
with the corresponding methods designed for conventional images 3 29 14 23 However, due to the ill-posedness of the problems they face, the quality of their results is still limited.
Considering the fact that different types of degraded polarized snapshots would provide complemen- tary knowledge, i.e., the short-exposure noisy ones tend to be clear while the long-exposure blurry
Most of this work was done as a PhD student at Peking University.
Corresponding author.
polarized snapshot consists of four polarized images with different polarizer angles (0", 45" ,90%, 135"), which can be captured using a polarization camera in single shot or using a polarizer in multiple shots.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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Complementaril fusing
457
DsP
nep
30
125
ArP
207 137
Arp
Noisy (short-exposure)
Blurry (long-exposure)
Clean and clear (fused)
In polarimetric imaging, since polarizer would block part of the light, setting a short exposure time would result in a low SNR, making the DoP and AoP severely degenerated (leff); while if setting a relative long exposure time to increase the SNR, motion blur more likely to occur, making the DoP and AoP over-smoothed (middle). Our framework can produce clean and clear results with high-qualin DoP and AoP by complementarily fusing a degraded pair of noisy and blurry polarized snapshots (right).
Figure 1:
ones tend to be clean, an intuitive strategy to improve the quality of polarimetric imaging could be complementarily fusing degraded pair of noisy and blurry polarized snapshots. Such strategy can not only achieve an effect similar "boosting" (i.e., combining multiple weak ones into strong ones) to produce clean and clear results, but also bring the existing degraded polarized snapshots alive. However, current methods that can fuse noisy and blurry pairs [17 28 are designed for conventional images, which are not suitable for polarimetric imaging since they cannot preserve the polarization properties, resulting in inaccurate DoP and AoP.
In this paper, we propose quality-improved and property- preeseved polarimetric imaging framework that can produce clean and clear polarized snapshots by complementarily fusing degraded pair of noisy and blurry ones, as shown in Fig. D (right). Specifically, we design neural network-based phree- fusing scheme that can explicitly take the preservation polarization properties into consideration. The first phase is irradiance restoration, aiming to restore the cetrrizatiiouunrelatt high-level irradiance information of the scene by recovering the total intensity of the light, where the color and structure cue fusion (CSCF) module is proposed to make full use of the color and structure cues encoded in the Stokes parameters. The second phase is polarization reconstruction, aiming to establish the physical correlation between the polarized images by reconstructing the DoP and AoP, where the coherence-aware aggregation (CAG) and coherence injection (CI) modules are proposed to optimize the values of the DoP and AoP in Cartesian coordinate representation. The third phase is artifact suppression, aiming to suppress the artifacts lying in the details by performing refinement in the image domain. Unlike the fusing methods designed for conventional images 21 22 28), our framework can fully utilize the complementary knowledge from the noisy and blurry pairs in polarization-awee aware manner, by virtue of our three-phase fusing scheme. Different from the polarized image enhancement methods 33 33
designed for enhancing a single noisy or blurry polarized snapshot, framework can effectively explore the usage of different physical quantities to improve the overall performance, thanks to the epesially-designed modules tailored to each phase. To summarize, this paper makes contributions by demonstrating:
A
and -rreeere- polarimetric imaging framework, for the first time applying fusing strategy to polarimetric imaging.
A neural network-based three-phase fusing scheme, fully utilizing the complementary knowledge from the noisy and blurry pairs in a polarization-aware manner.
Specially-designe modules tailored each phase, effectively exploring the usage of different physical quantities to improve the overall performance.
2
Related work
Low-light enhancement and deblurring for polarized images. There are many methods specially designed for enhancing polarized images, aiming to improve the quality of polarimetric imaging.

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IPLNet [00] and ColorPolarNet (25] adopted residual dense blocks to build the backbone for dealing with multiple polarized low-light noisy images simultaneously. Li et al. [15] proposed noise modeling method for realistic polarized low-light data synthesis along with powerful vision Transformer-basee network structure to reduce the noise. PLIE [32] designed a novel Stokes-domain low-light enhancement strategy and proposed a dual-branch network to reduce the artifacts lying in the DoP and AoP. PolDeblur (33] proposed a polarized image deblurring pipeline along with a two-stage network to remove the motion blur in a polarization-awan manner. However, they are not good at recovering details due to the ill-posedness of the problem they face.
Image enhancement by fusing noisy and blurry pairs. In comparison with the image enhancement methods that only take single degenerated image as the input (e.g., low-light enhancement 29] or deblurring [14 [33 methods that focus on processing either single low-light noisy image or single blurry image), fusing noisy and blurry pairs could usually achieve higher performance and better generalization ability since additional information can be acquired. Early works are usually based on numerical optimization. Yuan et al. [26] adopted residual deconvolution process along with gain-controlled deconvolution process to reduce the overall ringing artifacts during fusing. Choi et al. [4] designed a novel camera system that could capture two blurry images and one noisy image in a single shot, and proposed motion- based image merging algorithm to merge the captured images into a high- high-quality one. Son and Park [22] proposed a patches- based point spread function (PSF) estimation approach by extracting the structure information from the noisy image, along with a channel-dependent deblurring method to obtain the blur-free image. Son et al. [1] proposed a scheme to alternatively estimate the PSF and perform the deconvolution operation on the blurry image using the noisy image as a guiding signal. Gu el al. 77] proposed a method based on Gaussian mixture model to estimate the underlying intensity distribution of the noisy and blurry pairs first and then perform the pixel fusing. Recently, deep neural networks have also been adopted to handle this problem. LSD2 [17 and LSFNet [2] proposed to use convolutional neural networks to fuse the images in an end-to-end manner. SelfIR (27] proposed a self-supervised learning strategy to restore the clean and clear image contents. D2HNet (28) adopted two-phase pipeline to further increase the visual quality. However, the above methods are designed to enhance the quality of a single input image, which would show inferior performance when handling multiple polarized images.
Method
3.1 Problem formulation and overall framework
As shown in Fig. D our goal is to reconstruct a clean and clear polarized snapshot with preservation of polarization properties (denoted as I [... from a degraded pair of noisy and blurry polarized snapshots (denoted as = 1.,22,344 and B = 20,22444 respectively). where 01,2,3,4 0", 45" 90", 135" stand for the polarizer angles of the polarized images in the polarized snapshot respectively. Once I becomes available, high-quality DoP p and AoP 0 could be calculated using
S
1
Sg S
p
and 0 - aretan
(1)
So
where S,,1, are called the Stokes parameters 13 which can be computed as
So = [I, Ia, + lay + Iaa) = Ia, + + = Ioz
+ Loa
(2)
S = Ing Iaj
S2 las Loz
Here, we can see Sn describes the total intensity of the light, which is polarivation-unnelated. In the following, we will use $/,12 and $i,12 to denote the Stokes parameters of L and B respectively.
The overall reconstruction process of our framework can be formulated as maximizing posteriori of the output I conditioned on the inputs L and B along with the fusing function f parameterized by tr:
argmax / SII
Mooe information about the Stokes parameters could be found in the supplementary material.
3

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sish
cisc
F
Mulliscale color & structure feelures
Fims
CAG
Coherence volumes
Fnc
Phase1: Irradiance restoration
Phase2: Polarization reconstruction
Add Compute
Feature merging
U-net backbone
Merged dual-branch
Color structure
CSCF: color and structure cua fusion
encoder
Festure downlup- sampllnn
CAG: cohorenco-awane aware eggregalion
Fmer
Danse blocks
Cl: coherence injection
Phase3: Artifact suppression
Figure 2: The workflow of our framework, consisting of three phases: irradiance restoration, polar- ization reconstruction, and artifact suppression.
To solve this maximum a posteriori estimation problem, we design a neural network-based three- phase fusing scheme to implement the fusing function f. as shown Fig. 2 First, the irradiance restoration phase restore the polarization unrelated high-level irradiance information of the scene, by enhancing 8 obtain the coarse value of the total intensity of the light S under the guidance of the color and structure cues provided by S and S respectively. Then, we compute (x', y'), which are the coarse values of the DoP and AoP in a Cartesian coordinate representation, and feed them into the polarization reconstruction phase to obtain the corresponding enhanced values (x', , y") with the help of (xB y (the DoP and AoP of in Cartesian coordinate representation) along with the irradiance clues encoded in S aiming to establish the physical correlation between the polarized images. Finally, we compute the coarse values of the polarized images I',, 2 and adopt an artifact suppression phase to obtain L,y,,,.4 that make up the clean and clear polarized snapshot I, by suppressing the artifacts in the image domain for increasing the quality of details.
Phasel: Irradiance restoration
This phase aims to restore the polarization iasiiioonnummtttt unrelated high-level irradiance information for providing further guidance. As shown in Fig. T. since would retain better contours than B, propose to learn the residual between S and S instead of the residual between D and Sh. However, S usually suffers from color bias and noise, which would increase the difficulty of feature extraction, resulting in erroneous global tone and less salient local structure. Fortunately, despite that SB would suffer from motion blur, it still contains undamaged color information due the relatively high SNR of B; besides, Sh.2 could provide distinctive structure information since both of them describe the difference between two polarized images (see Eq. (2) which would highlight the regions with high gradients. Therefore, we propose to effectively explore the usage of S and S
Specifically, first explicitly adopt two modal-specific feature encoders F and Fs to extract the multiscale color and structure features F and Fi,2,3 from Si and S respectively for guidance. Then, propose
three color and structure cue fusion (CSCF) modules to apply the guidance provided by Fi.23 and Fi,2.3 to Fip,, a successive manner, and output F for restoring Sb. Here, Fin and Four 1,2.3 denote the multiscale input and output features of the CSCF modules respectively, which are extracted from and fed the encoder and decoder part of a modified autoencoder architecture
9 where dense block [ is inserted into the coarsest layer.

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(-th scale
color feature
F
4-th scale
structure
F
CSCF
(a)
CAG
(b)
X
feature
Bottleneck
Bottlenack
Bottlenack
Bottleneck
Bottleneck
Bottleneck
CAT
CAT
Conv
Conv
Conv
Conv
Conv
Z₂
(M,C,H,))
Zy
Conv
Sigmold
Offset
Modulator
i-h scale
(-th scale output feature
Pool
Muttiply
Pool
feature
input
m
AP,
AM
MLP
MLP
Sigmaid
(N.C.8,0)
Sigmoid
Fin
Deformable Conv
F
(K.C,1,1)
Fy
(1.C,11)
Mutiipyy
Add
Coherence volumes
Figure 3: The details of the proposed CSCF (color and structure cue fusion) and CAG (coherence- aware aggregation) modules.
CSCF: color and structure cue fusion. The CSCF module aims address the issues erroneous global tone and less salient local structure in the feature space. Without losing generality, we describe how the i-th scale (i = 1, 2, 3) CSCF takes Fü, F;, and F? as the input and output F?"., as shown in Fig. 3 (a). We first learn multiplier m, and a bias b, from F; by
m; Ba (Sigmoid(Fi))) and b; (,(C,(FF)),
where B. denotes a bottleneck block [8] used for feature projection, Cm and C. denote two different convolution layers. Then, we apply affine transformation F using m, and b; adjust the color in the feature space for solving the issue of erroneous global tone by
F m, F.P + bb,,
(5)
where F; denote the transformed feature, O denotes element-win product operation. Finally, to solve the issue of less salient local structure, apply deformable convolution layer (4 D to align the gradients and overcome the possible shifts caused by the exposure interval in the feature space by
F = D(F), AP;, AM,,
where AP; and AM; the offsets of sampling points and the modulation scalars learned by
AP; B, (C)()))) and AM, B2 (Fi),
(7)
where B. Op, and Cm denotes another bottleneck block
8 and convolution layers respectively.
3.3 Phase2: Polarization reconstruction
This phase aims to establish the physical correlation between the polarized images by reconstructing the high-quality DoP and AoP. To achieve it, previous methods usually choose to repair the degen- crated values in the image domain [10] 25
Unit circle
15 33) or Stokes domain 32] for indirect reconstruction, since the degeneration patterns of the DoP and AoP could be more complicated than the polarized images Stokes parameters due their non- coneaiieayyty (see Eq. (I), which could increase the ill- poseposesssss. In contrast, we propose to re- construct the DoP and AoP in Cartesian coordinate representation, which can not only relieve the ill-posedness since the non-linearity reduces, but also optimize the values of the DoP and AoP in a direct manner to prevent error accumulation.
20
||$| =p < S 20
Here, explain what is the Cartesian coordinate representation of the DoP and AoP: as shown in Fig. 4 we regard and 20 Eq. (1 as the magnitude and angle of vector Š lying inside a unit circle, the Cartesian coordinate representation of S could be written
Figure 4: The Cartesian co- ordinate representation of the DoP and AoP.
as (x, y), which satisfying
S So
S₂ and y =
x
(8)
So
5

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Specifically, we propose to learn the residual between (x'.y') and x'),,,,, with the help of (²) and S. where
S S
S S
S S
and B
S
First, we propose use coherence-awand aggregation (CAG) module to estimate the coherence volumes Fx and F. from xB,, yB and Si. Then, we adopt two branches for reconstructing x' and y' respectively. The first branch contains feature encoder Fèse and three cascaded coherence injection (CI) modules using Fx for guidance. Similarly, the second branch contains a feature encoder F and three cascaded CI modules using F, for guidance.
CAG: coherence-aware aggregation. The CAG module aims aggregate the priors about the coherence between the polarization properties and the irradiance information. As shown in Fig. (b), it contains two symmetrical parts for estimating F, and F, respectively. Here, we only describe how to estimate Fx since the estimation process of Fy could be similar. We first adopt two bottleneck blocks [ to extract polarization features and irradiance features from xB and Sy respectively. Then, we project the extracted features into the coherence features Z₃ E TR-xxCxH>* convolution layer, where N, C, H, W represent the batch size, number of channels, height, and width respectively. After that, inspired by CBAM (24) that can make full use of the inter-channel relationship of features, we propose to learn an attention vector Ax E E xxxxxx recalibrate Zx for obtaining F, E IR IgNxxxXXxW
using a
F. A. Z = P(MLP(Signoid(Z.)) @ Zx,
(10)
where P denotes the global average pooling operation and M MP denotes a multi-layer perceptron.
Cl: coherence injection. The CI module aims to inject the priors about coherence into the recon- struction of x' and y'. To enlarge the receptive field and include long-range association, we choose to use Transformer modules 6 with cross-attention layers. Taking one of the CI module in the first branch (the branch for reconstructing x') as an example, denoting its input as F (from the previous CI module or Fane) and Fx (from the CAG module), we let Fir to serve as the query vector and adopt convolution layers to learn the key vector and the value vector from both F and F..
3.4 Phase3: Artifact suppression
With Sh and (x', y') available, we could compute the coarse values of the polarized images 2,0," However, we should not output 2,,, directly since their quality is still not satisfying. This is because S/ and (x', are estimated from two different phases so that the irradiaceeppolariaatoo polarization consistency would break, bringing artifacts to the details. Therefore, we add an extra phase to refine 121....4 for increasing the quality of details by suppressing the artifacts in the image domain.
Specifically, propose learn the residual between Va and 2.,.2.3.4 According Eq. (
choose to divide V Va,, into two groups (I',,, and I first ensure both of them contain the full irradiance information and each of them contains half of the polarization properties. Then, use two convolution layers to extract the features of K',,, and V'22,1 respectively, and adopt a feature merger Fmer to obtain the merged dual-group features F mer. After that, a U-Net backbone [18) is used perform pixel-wise multi-scale feature refinement on F mer. and another two convolution layers are adopted for decoding the refined dual-group features into the residuals of each group.
4 Implementation details
Loss function. The total loss function can be written as
L= Lg + Lp + L,,
(11)
which consists of three terms to optimize the three phases respectively: irradiance loss L,, polarization loss Lp. and refinement loss L, The irradiance loss could be written as
L =
s + X L.pecc (S',, )
(12)
where Xab are set be 10.0 and 0.05 respectively, L, and I Eper denote the l loss and perceptual loss respectively, the subscript gt labels the ground truth throughout this paper. The perceptual loss

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Table 1: Quantitative comparisons on synthetic data. The comparisons involve our framework, the state-of-the- polarized image low-light enhancement method PLIE [32 and improved version
PLIE+, the only existing polarized image deblurring method PolDeblur 33 and its improved version
PolDeblur+, and four learning- -aagd--bbdddd-e that also fuse noisy and blurry pairs (LSD2 [17], LSFNet [2]. SelfIR [27]. and D2HNet (28))
image enhancement methods designed for conventional images
PSNR-p
SSIM-p
PSNR-0
SSIM-0
PSNR-Sp
SSIM-S,
Ours
29.23
0.797
16.96
0.382
39.05
0.982
PLIE
32
27.91
0.790
15.92
0.371
38.95
0,978
PLIE+
27.98
0.794
16.93
0.379
39.01
0,979
PolDeblur
33
24.52
0.676
15.73
0.280
26.12
0.794
PolDeblur+
25.31
0.758
16.75
0.374
39.04
0.981
LSD2 17
25.73
0,662
13.75
0.288
27.88
0,905
LSFNet 2
25.56
0.693
15.90
0.282
26.76
0,826
SelfIR 277
19.43
0.647
15.39
0.231
25.90
0.785
D2HNet 28
24.45
0.671
15.63
0.264
25.25
0.803
Lpere is defined as
Lee (S): Sh) L2(0n (n (Sh)),
(13)
where Le denotes the le loss, on denotes the feature map from h-th layer VGG-19 network [20] pretrained ImageNet [19], and we use activations from VGG3,3 convolution layer here. The polarization loss could be written as
Lp = ( x + Li(y', y ) + (x') (y)) + pa xx!, xx'."" y', yst)
(14)
where Aghe are be 1.0, 0.15, and 1.0 respectively, Tay denotes the total variation loss, pll is polarization-base regularization term ensure the ratio between x' and y' defined
4e (x, x ,', La(x's O y о x8)).
(15)
The refinement loss could be written as
L X (101224
Es 1 X L2 (T (Lm1,2a))
(16)
where Aath set to be 10.0 and 100.0 respectively, 4i00 denotes another polarization-batt based regular- ization term defined as
2 (Ian (a.))).)) = L2(Ia, Ia. Iap + Ias).
(17)
which is similar to the one used in 33 for enforcing the preservation of polarization properties.
Dataset preparation. We propose to generate a synthetic dataset due the fact that there is no public dataset for our settings. First, we choose the PLIE dataset [32) as our data source. It provides short-exposure polarized snapshots that suffer from low-light noise along with the corresponding high-quality reference snapshots captured by Lucid Vision Phoenix polarization camera, which could serve as L and Z. Then, we adopt the approach proposed in 33 to generate the blurry polarized snapshots that suffer from motion blur, which could be served as B. To generate more severe motion blur for increasing the diversity, we add impulsive variation [ to the motion trajectories. The images resized and randomly cropped to 256 x 256 (512 512) pixels in the training (test) set. The training (test) set contains 7500 (300) different images total.
Training strategy. Our framework is implemented using PyTorch with NVIDIA 2080Ti GPUs, and two-stage training strategy applied. First, ensure stable initialization of the training process, we train the irradiance restoration phase and the polarization reconstruction phase independently for 300 epochs with learning rates 0.01 and 0.0001 respectively. Then, we train the entire network for 100 epochs with learning rate of 0.0001, and in this training stage we multiply the loss terms Laps
with 5.0, 10.0, and 10.0 respectively. For optimization, we use Adam optimizer 12 with 31 = 0.5. 82 = 0.999.
7

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Noisy
Blury input
Reference
Ours
PLIE
PolDeblur
P
PolDeblur
LSD2
LSFNet
SeifIR
D2HNet
Noisy input
Blury Input
Reference
PLIE
PolDeblur
o
PLIE+
PolDeblur
LSD2
SelfIR
D2HNet
Noisy input
Blurry inpul
Reference
PoiDablur
So
PLIE
PoiDeblur+
LSD2
DZHNet
Figure 5: Qualitative comparisons synthetic data. See the caption of Tab. for explanation. We visualize the DoP p and AoP using color maps after normalizing and averaging the RGB channels (as done in other methods designed for polarized images [00 25
33
throughout this paper.
Experiments
5.1 Evaluation synthetic data
First, we compare our framework with the state-of-the-art polarized image low-light enhancement method PLIE 32 and the only existing polarized image deblurring method PolDeblur [33] Besides, we also compared with PLIE+ and PolDeblur+ (the improved versions of PLIE 332 and PolDeblur 33, where slight modifications input) to ensure a fair comparison. In addition, four learning-based image enhancement methods designed for conventional images that also fuse noisy and blurry pairs (LSD2 [77, LSFNet (2). SelfIR (27), and D2HNet (28)) are also compared to ensure comprehensive evaluation. Note that all compared methods retrained on our dataset. As other methods designed for polarized images
made allow them accept noisy and blurry pairs as the
[10 25 15 32 33 do, we not only evaluate the quality of p and 0, but also the quality of Sp.
To evaluate the results quantitatively,
adopt frequently-use -used metrics including PSNR and SSIM. Results are shown in Tab. [ where our framework consistently outperforms the compared methods all metries. These results could demonstrate three points:
(1) Complementarily fusing can improve the quality of polarimetric imaging, which could be deduced from the fact that PLIE+ and PolDeblurt (which can accept a degraded pair of noisy and blurry polarized snapshots as the input) achieve better performance compared with PLIE (32 and PolDeblur 33 (which can only accept single degraded polarized snapshot the input) respectively.
(2) Our frumework can utilize the complementary knowledge in more effective manner, since our framework still outperforms PIIE+ and PolDeblur+ despite that they share the same kind of input our framework.

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Noley input
Blurry input
Reference
Ours
PLIE
PolDeblur
p
PLIE+
PolDeblur
LSD2
LSFNet
SeilIR
D2HNet
input
Blurry
Reference
PLIE
PolDablur
P
PolDeblur
LSD2
LSFNet
SellIR
D2HNet
Input
Blurry
Reference
PolDeblur
So
PUIE+
PolDeblur
LSFNet
SelfIR
DZHNet
Figure 6: Qualitative comparisons real data. See the caption of Fig. 5 for explanation.
(3) Designing a fusing framework tailored to the polarized images is necessary, since the performance of both LSD2 [17]. LSFNet 22, SelfIR (27, and D2HNet 28 is inferior in the task of polarimetric imaging.
Visual quality comparisons are shown Fig. As p and 0, our framework can produce clean and clear edges, since it can make full use of the complementary knowledge in polarization-ave manner, while the compared methods suffer from noisy or blurry artifacts. As for Sp, our results resemble the reference more closely with less color and structure distortion.
5.2 Evaluation on real data and downstream application
To evaluate on real data, we capture several pairs of noisy and blurry polarized snapshots from various scenes using Lucid Vision Phoenix polarization camera. Qualitative results are shown in Fig. from which we can see our framework can produce high-quality details.
Besides, in Fig. we show that complementarily fusing be beneficial downstream polarization- based vision application such as reflection removal. Here, we feed a short-exposure noisy. long- exposure blurry, and the fused polarized snapshots into reflection removal network (RSP [66] respectively. From the results we can see the rerectiion-rmoveedd image with the fusing process of our framework contains more detailed textures and less reflection contamination.
5.3
Ablation study
To verify the validity of each design choice, conduct series of ablation studies and show comparisons in Tab. First, we show the effectiveness of the first phase by substituting with
Additioonl results can he found supplementary material. 'Please the supplementary material for additional results.

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Noisy
Blumy
Fused by our framework
Noisy
Blury
Fused by our framework
Rellection-cotaamiatte Input
Reflection-removed output
Figure 7: Results of reflection removal (using RSP [66
Please zoom-in for better details.
Table 2: Quantitative evaluation results of ablation study.
PSNR-p
SSIM-p
SSIM-8 PSNR-9
PSNR-Sp
SSIM-Sp
LSD2 17
as Phasel
29.12
0.794
16.91
0.376
38.98
0,980
W/o CSCF
29.21
0.796
16.93
0.378
38.94
0.978
W/o CAG
29.07
0.793
16.87
0.371
38.97
0.980
W/o CI
28.92
0.788
16.90
0.371
38.90
0.976
W/o Cartesian
28.04
0.785
16.58
0.363
38.84
0,971
W/o refinmment
29.02
0.791
16.84
0.367
38.89
0.976
Complete framework
29.23
0.797
16.96
0.382
39.05
0.982
Sranning-based image enhancement methods designed for conventional images (LSD2 17 as Phasel). The reason why we choose LSD2 [17 is that it outperforms other similar methods (LSFNet (2) SelfRR (27]. and D2HNet (28)) in restoring So (see Tab. D.. We can see that the performance becomes inferior since our first phase can make full use of the color and structure cues encoded in the
Stokes parameters while LSD2 17 cannot. Then, we show the effectiveness of the proposed CSCF modules in the first phase (W/o CSCF) by substituting them with vanilla convolution layers. We can see that the performance degenerates since the CSCF modules are more suitable for addressing the issues of erroneous global tone and less salient local structure in the feature space. Similarly, we also show the effectiveness the proposed CAG module and CI modules in the second phase (W/o CAG and W/o CI). We can see that the CAG module can facilitate the establishment of the physical correlation between the polarized images, and the CI modules can offer better optimization to values of the DoP and AoP. Besides, demonstrate the advantage of reconstructing the DoP and AoP in a Cartesian coordinate representation (W/o Cartesian) by directly reconstructing their values. We can that the performance degraded severely duc to the non-linearity. Finally, we verify the necessity of the third phase used for refinement (W/o refinement) by removing it. These results show complete framework achieves the first performance with the proposed specific designs.
Conclusion
We propose quality -improved and property- prreeeeed polarimetric imaging framework by com- plementarily fusing degraded pair of noisy and blurry polarized snapshots. By adopting a neural network-based based three-phase fusing scheme consisting of irradiance restoration, polarization reconstrue- tion, and artifact suppression, with specially-designer modules tailored each phase, our framework can produce clean and clear polarized snapshots with high-quality DoP and AoP.
Limitations. Since framework is designed for reconstructing single high-quality polarized snapshot from degraded pair of noisy and blurry polarized snapshots, it cannot reconstruct polarized video. Besides, cannot be used fuse conventional RGB images since our first phase requires the Stokes parameters as part of the input, which are not available in such a setting.
Acknowledgments and Disclosure of Funding
This work was supported in part by National Natural Science Foundation of China under Grant No. 62136001 62088 102, 62276007 and JST-Mirai Program Grant Number JPMJMI23GI.
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A Appendix
Please see the supplemental material for the things mentioned in Footnote 2, 3, and 4.
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Reviews:
[{"review_id": "rK7y09UVk9", "reviewer": "Reviewer_4C9V", "summary": "This paper proposes the first method for polarimetric image enhancement by fusing noisy and blurry pairs. While a short exposure polarimetric image produces sharp but noisy DoP and AoP, a long exposure makes them smooth but blurred. To effectively exploit the complementary advantages of these two images and satisfy the physics constraints of the polarimetric image, this paper proposes a three-phase fusing scheme. Experimental results show that the proposed method outperforms existing polarimetric image enhancement methods.", "questions": "- Why does not the proposed method significantly improve the SSIMs of DoP and AoP? How does the improvement of PSNR affect the downstream tasks?\n- How are reference images of real data obtained? Can they be used for quantitative evaluation?\n- The visual comparisons of the ablation study will help understand the effectiveness of each component.", "limitations": "Yes.", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "+ The first method for polarimetric image enhancement by fusing noisy and blurry pairs.\n+ Propose a novel fusing scheme to effectively use complementary polarimetric information of noisy and blurry pairs and retain polarimetric cues by directly processing DoP and AoP.\n+ Experimentally validate the effectiveness of the fusion of noisy and blurry polarimetric image pairs and the proposed network. The accurate restoration of polarimetric cues is critical for downstream tasks.", "weaknesses": "- While the proposed method improves the pSNR of DoP and AoP, their SSIMs are almost the same as PLIE [32].\n- Requiring two shots is undesirable for some downstream tasks.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## Reviewer 4C9V\n\n* Issues about the PSNR and SSIM values of the DoP and AoP.\n  * PSNR is highly sensitive to small changes in pixel values, whereas SSIM considers structural information and spatial relationships within the image. Our method leverages the clean information from the blurry input, effectively reducing the noise level in the DoP and AoP, particularly in high-value regions, leading to higher PSNR scores compared to other methods. However, since the overall pixel values of the DoP and AoP are typically very small (much smaller than those of the images), structural details are usually significantly degraded (due to distortions in the low-value regions) and challenging to correct. In such situations, neither our method nor the compared methods can significantly improve the structural details, resulting in similar SSIM scores. Consequently, the improvement in SSIM is not as pronounced as in PSNR.\n  * Generally, an improvement in PSNR can be positively correlated with the quality of downstream tasks. This is because higher PSNR indicates better preservation of polarization information, which can provide more accurate polarization cues for downstream tasks. However, the quantitative relationship between them cannot be precisely determined, as the quality of downstream tasks significantly depends on the specific methods designed for those tasks. \n* Issues about the reference images of real data.\n  * See **common issues 1**.\n* Visual comparisons of the ablation study.\n  * We take the scene in Figure 5 as an example, which can be found in **the attached PDF file** (Figure A). We can see that although there is not much difference compared to other ablation items (due to their similar quantitative scores), there is still a slight advantage in details such as cleaner background.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "DSHQLQhJBG", "reviewer": "Reviewer_SSTW", "summary": "This paper proposes a polarimetric imaging framework that can produce clean and clear polarized snapshots by complementarily fusing a degraded pair of noisy and blurry ones. It adopts a neural network-based three-phase fusing scheme with specially designed modules tailored to each phase, which can not only improve the image quality but also preserve the polarization properties.", "questions": "It seems that using polarizers instead of polarization cameras can also capture the polarized images. However, in some cases one can only use a polarizer to capture polarized images instead of a polarization camera. Can the proposed method be used to process the data captured using polarizers?", "limitations": "The authors have adequately addressed the limitations.", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The idea of using complementarily fusing to achieve quality-improved and property-preserved polarimetric imaging is novel and reasonable. As obtaining high-quality polarized images is significant in polarization-based vision applications, while previous methods based on single modality (either noisy or blurry) tend to suffer from various artifacts, the proposed method could be a practical way to increase the performance of polarization-based vision applications.\n\nThe network module designs are also reasonable. All modules (Irradiance restoration, Polarization reconstruction, and Artifact suppression) are carefully and specially designed to solve the problems in the fusing process, which means the authors do spend efforts in observing and analyzing the properties in both the noisy and blurry polarized snapshots. \n\nThe idea is clearly presented, and the experiments are sufficient. The performance improvement shows that the proposed method is effective.\n\nIn addition to the experiments on synthetic and real data, the authors also show the results of reflection removal, which makes the paper convincing.", "weaknesses": "The authors say that they adopt the PLIE dataset [32] as the source data to generate their own dataset. However, they do not tell the reasons why to choose the PILE dataset [32]. For example, [25] also provides a dataset (LLCP dataset) similar to the PLIE dataset [32], so why not choose the LLCP dataset as the source data? Any reasons?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## Reviewer SSTW\n\n* Why not choose the LLCP dataset as the source data?\n  * This is because the quality of PLIE dataset [32] used in our paper could be better than the LLCP dataset [25]. For example, overexposed regions often appear in the reference images of the LLCP dataset [25]. Training a network with such data will reduce its generalization ability.\n* Can the proposed method be used to process the data captured using polarizers?\n  * Yes, it is theoretically feasible, as long as we can obtain four polarized images of the same scene with different polarizer angles ($0^{\\circ}, 45^{\\circ}, 90^{\\circ}, 135^{\\circ}$). However, using polarizers can only capture a single polarized image in a single shot, which is less convenient compared with using polarization cameras.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "FtSjKBY8Zu", "reviewer": "Reviewer_WQ4j", "summary": "This paper proposes a method to fuse a pair of short-exposure (noisy) and long-exposure (blurry) captures to produce clean and clear polarized snapshots. The proposed method consists of three phases to reconstruct the irradiance, texture, and polarization.", "questions": "1. When generating the synthetic dataset, what are the short and long exposure times? Have you considered different exposure time settings and varying motion blur intensities? Have you added sensor noise to the synthetic images?\n\n2. How is the reference image obtained when conducting real-world experiments (Fig. 6)? There are few details about the real-world experiments in the paper.\n\n3. In Fig. 7, is it possible to add comparison results from other methods? It is difficult to evaluate the final results solely based on the proposed framework. Also, how should one understand the difference between the “reflection-contaminated input” and the “reflection-removed output”? Again, there are few details about the real-world experiments.\n\n4. In line 56, it is not accurate to claim that this is “the first time applying a fusing strategy to polarimetric imaging.” There are existing pieces of literature on polarimetric image fusion, such as “Semantic-guided polarization image fusion method based on a dual-discriminator GAN” by Liu et al., and “Polarization-driven semantic segmentation via efficient attention-bridged fusion” by Xiang et al.", "limitations": "Limitations of this paper are well discussed.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "The paper is well-written, the proposed method is well-described, and experiments using both synthetic and real-world data are conducted to evaluate the effectiveness of the proposed method.", "weaknesses": "It is difficult to fully understand and evaluate the real-world experiments. Please refer to the corresponding questions for further details.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## Reviewer WQ4j\n\n* Issues about the synthetic dataset.\n\n  * The information can be found in Line215-223. Our synthetic dataset is generated from the PLIE dataset [32] (a dataset about polarized image low-light enhancement), which provides short-exposure ($T_{short}$) polarized snapshots that suffer from low-light noise (serve as $\\mathcal{L}$) along with the corresponding long-exposure ($T_{long} \\approx 10T_{short}$) high-quality reference snapshots (serve as $\\mathcal{I}$) captured by a Lucid Vision Phoenix polarization camera with a tripod. We only generate the blurry polarized snapshots ($\\mathcal{B}$) by ourselves.\n  * As for the exposure time, since $T_{short}$ varies across the PLIE dataset [32] dataset, our synthetic dataset could cover a long range of different exposure time settings. As for the ratio between $T_{long}$ and $T_{short}$, since the PLIE dataset [32] fixes the ratio to about $10$, we cannot change it during the generating process of our synthetic dataset. However, we believe our method can still have the generalization ability to different ratios, since we have the blurry polarized snapshots as the input, which can directly provide the information about the ratio.\n  * As for the motion blur, we have considered varying motion blur intensities. We adopt the approach proposed in [33] to generate the blurry polarized snapshots, which can generate different motion blur intensities and patterns. Besides, to generate more severe motion blur for increasing the diversity, we add impulsive variation [1] to the motion trajectories.\n  * As for the sensor noise, since the images in PLIE dataset [32] are captured by a real polarization camera, they already include real sensor noise. Therefore, we do not need to add synthetic noise into the images.\n\n* Issues about the reference images of real data.\n\n  * See **common issues 1**.\n\n* Issues about Figure 7.\n\n  * We provide the comparison results from other methods in **the attached PDF file** (Figure B). We can see that the reflection-removed image with the fusing process of our framework contains more detailed textures and less reflection contamination than other methods.\n\n  * In Figure 7, we feed a short-exposure noisy, a long-exposure blurry, and the fused polarized snapshots into a reflection removal network (NIPS19RSP [16]) respectively, and obtain the corresponding output images respectively.  The label \"reflection-contaminated input\" denotes the scenes fed into the reflection removal method [16], and the label \"reflection-removed output\" denotes the output scenes from the reflection removal method [16] respectively.\n  * The capturing process of the scenes in Figure 7 is similar to the real data shown in Figure 6, please refer to **common issues 1**.\n\n* Issues about our claim.\n  * Here we explain the differences between our claim and the papers mentioned in the reviews separately:\n    * The claim of \"the first time applying a fusing strategy to polarimetric imaging\" in Line56 of our paper is about polarimetric imaging. Note that the term \"polarimetric imaging\" means outputting high-quality polarized snapshots captured by polarization cameras. Since existing methods designed for such a goal do not use the complementarily fusing strategy, our claim could be accurate.\n    * The term \"polarization image fusion\" in the paper named as \"Semantic-guided polarization image fusion method based on a dual-discriminator GAN\" is the process of fusing an intensity image and a polarization parameter image solved by Stokes vector into a more detailed image. It means outputting unpolarized images with more details, which is about increasing the quality of intensity images.\n    * The term \"attention-bridged fusion\" in the paper named as \"Polarization-driven semantic segmentation via efficient attention-bridged fusion\" is fusing polarization information into the semantic segmentation procedure, which is about network designing.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
## Common issues 

We sincerely thank all reviewers for their valuable comments and suggestions. We feel encouraged that the novelty and performance of our method are acknowledged by the reviewers:

* Propose a novel fusing scheme to effectively use complementary polarimetric information of noisy and blurry pairs and retain polarimetric cues by directly processing DoP and AoP. (**Reviewer 4C9V**)
* The idea of using complementarily fusing to achieve quality-improved and property-preserved polarimetric imaging is novel and reasonable. (**Reviewer SSTW**)
* The paper is well-written, the proposed method is well-described, and experiments using both synthetic and real-world data are conducted to evaluate the effectiveness of the proposed method. (**Reviewer WQ4j**)

We first address the common questions here as the **common issues**, and then answer each reviewer's specific questions in the corresponding comments. 

1. Issues about the reference images of real data. (**Reviewer 4C9V, WQ4j**)
   * The reference images of real data (in Figure 6) are captured as follows: 
     1. Use a tripod to fix the polarization camera.
     2. Use a program (written by the SDK of the polarization camera) to capture a short-exposure ($T_{short}$) polarized snapshot (as the noisy input $\mathcal{L}$) and a long-exposure ($T_{long} \approx 10T_{short}$) blur-free one (as the reference $\mathcal{I}$) consecutively. Note that this step is similar to the way of data capturing in [3].
     3. Remove the tripod, hold the polarization camera by hand (which brings about motion blur), and capture another long-exposure (also $T_{long}$) polarized snapshot (as the blurry input $\mathcal{B}$).
   * These real data can also be used for quantitative evaluation. Taking the scene in Figure 6 as an example, the quantitative scores are shown below:

|                | PSNR-$\mathbf{p}$ | SSIM-$\mathbf{p}$ | PSNR-$\theta$ | SSIM-$\theta$ | PSNR-$\mathbf{I}$ | SSIM-$\mathbf{I}$ |
| -------------- | ----------------- | ----------------- | ------------- | ------------- | ----------------- | ----------------- |
| Ours           | 30.11             | 0.774             | 19.17         | 0.441         | 35.45             | 0.973             |
| PLIE [32]      | 28.97             | 0.771             | 18.74         | 0.399         | 34.13             | 0.971             |
| PLIE+          | 28.73             | 0.765             | 18.69         | 0.407         | 35.24             | 0.973             |
| PolDeblur [33] | 27.19             | 0.730             | 18.53         | 0.426         | 35.12             | 0.958             |
| PolDeblur+     | 27.98             | 0.747             | 19.05         | 0.437         | 35.38             | 0.969             |
| LSD2 [17]      | 25.76             | 0.563             | 13.45         | 0.368         | 16.58             | 0.906             |
| LSFNet [2]     | 25.99             | 0.681             | 18.28         | 0.421         | 33.41             | 0.938             |
| SelfIR [27]    | 22.21             | 0.720             | 17.26         | 0.376         | 35.37             | 0.940             |
| D2HNet [28]    | 25.64             | 0.683             | 17.54         | 0.385         | 28.89             | 0.863             |

Meta-review: This paper receives one strong accept and two weak accept. This paper proposes a complementary method to fuse a degraded pair of noisy and blurry ones to generate high-quality polarimetric imaging. In the rebuttal, the authors have adequately addressed most of the reviewers' major concerns. The authors are encouraged to revise the paper by adding a comparison of the computational cost.
Decision: Accept (poster)