SUShe: simple unsupervised shadow removal

Abstract

Shadow removal is an important problem in computer vision, since the presence of shadows complicates core computer vision tasks, including image segmentation and object recognition. Most state-of-the-art shadow removal methods are based on complex deep learning architectures, which require training on a large amount of data. In this paper a novel and efficient methodology is proposed aiming to provide a simple solution to shadow removal, both in terms of implementation and computational cost. The proposed methodology is fully unsupervised, based solely on color image features. Initially, the shadow region is automatically extracted by a segmentation algorithm based on Electromagnetic-Like Optimization. Superpixel-based segmentation is performed and pairs of shadowed and non-shadowed regions, which are nearest neighbors in terms of their color content, are identified as parts of the same object. The shadowed part of each pair is relighted by means of histogram matching, using the content of its non-shadowed counterpart. Quantitative and qualitative experiments on well-recognized publicly available benchmark datasets are conducted to evaluate the performance of proposed methodology in comparison to state-of-the-art methods. The results validate both its efficiency and effectiveness, making evident that solving the shadow removal problem does not necessarily require complex deep learning-based solutions.

Full text

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Multimedia Tools and Applications (2024) 83:19517–19539
https://doi.org/10.1007/s11042-023-16282-0
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SUShe: simple unsupervised shadow removal
Dimitra‑ChristinaC.Koutsiou1 · MichalisA.Savelonas1 · DimitrisK.Iakovidis1
Received: 16 November 2022 / Revised: 31 May 2023 / Accepted: 4 July 2023 /
Published online: 28 July 2023
© The Author(s) 2023
Abstract
Shadow removal is an important problem in computer vision, since the presence of shadows com-
plicates core computer vision tasks, including image segmentation and object recognition. Most
state-of-the-art shadow removal methods are based on complex deep learning architectures, which
require training on a large amount of data. In this paper a novel and efficient methodology is pro-
posed aiming to provide a simple solution to shadow removal, both in terms of implementation
and computational cost. The proposed methodology is fully unsupervised, based solely on color
image features. Initially, the shadow region is automatically extracted by a segmentation algorithm
based on Electromagnetic-Like Optimization. Superpixel-based segmentation is performed and
pairs of shadowed and non-shadowed regions, which are nearest neighbors in terms of their color
content, are identified as parts of the same object. The shadowed part of each pair is relighted by
means of histogram matching, using the content of its non-shadowed counterpart. Quantitative
and qualitative experiments on well-recognized publicly available benchmark datasets are con-
ducted to evaluate the performance of proposed methodology in comparison to state-of-the-art
methods. The results validate both its efficiency and effectiveness, making evident that solving
the shadow removal problem does not necessarily require complex deep learning-based solutions.
Keywords Shadow removal· Color· Histogram matching· Electromagnetism-like
optimization
1 Introduction
Core computer vision tasks, such as navigation and obstacle detection are complicated
in the presence of shadows, which can be misinterpreted as objects or obstacles. Several
methods have been proposed to address shadow detection and removal in various appli-
cation domains, including satellite imaging, traffic monitoring, and obstacle detection in
* Dimitris K. Iakovidis
diakovidis@uth.gr
Dimitra-Christina C. Koutsiou
dkoutsiou@uth.gr
Michalis A. Savelonas
msavelonas@uth.gr
1 Department ofComputer Science andBiomedical Informatics, University ofThessaly,
Papasiopoulou 2-4, 35131Lamia, Greece
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navigation systems [4, 28, 52, 57, 59]. Figure1 shows example images illustrating objects
in a shading environment.
The shadow problem is commonly treated using the Shadow Model Theory (SMT) pro-
posed by Barrow etal. [6], which enables the calculation of the intensity of light, reflected
at a given point on a surface. It is a physics-based model, which decomposes illumination
in two components: direct and ambient illumination. According to Guo etal. [23], the illu-
mination model for an RGB image is provided by:
where Ii is the color intensity of pixel i in R, G and B color channels, Ld and Le are the light
intensities associated with the light source and ambient sources respectively, θi is the angle
defined by direct lighting direction and surface, and ti ∈[0, 1] is a variable which denotes
the amount of light inside an area.
Early shadow removal methods, such as [7, 17–19, 36, 41], were also based on models
relying on a number of assumptions, and usually evaluated on datasets with a small number
of images, focusing mainly on qualitative aspects. Later, there was a decisive shift towards
supervised methods, such as deep neural networks, which have brought new trends, but
also the requirement for large training sets. New benchmark datasets were created, to cover
this requirement, and evaluations begun to encompass also a more quantitative aspect [33,
46, 50, 53]. A drawback was that in these datasets shadows needed to be manually anno-
tated, and such annotations are time-consuming and usually costly. Furthermore, deep neu-
ral networks are usually computationally expensive and demanding in terms of computa-
tional resources.
The state-of-the-art shadow detection and removal approaches can be divided into two
categories: a) unsupervised methods, and b) supervised methods. Most methods of both
categories encompass the SMT and use a coefficient to indicate the intensity in the shadow
areas based on Eq. (1). This coefficient describes the brightness reduction in relation to
the area of the image without any shadows [15, 35, 47] . Finding the right parameters that,
when multiplied by the intensity of each pixel in the shadow zone, the initial illumina-
tion will be recovered in the shadowed areas. Unsupervised methods are usually based on
intrinsic image features, such as color and texture, and strategies that enable the recovery
of detail and luminosity of shadow regions [5, 12, 16–19, 22, 25, 29, 31, 36, 41, 60, 63].
Supervised methods, are mainly based on complex deep learning architectures, and they
(1)
Ii
=
(
t
i
cos𝜃
i
L
d
+L
e)
R
i
(a) (b) (c)(d)
Fig. 1 Example images illustrating objects in shadowed environments(a-d) from various publicly available
shadow datasets considered in this study [4, 16, 17]
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usually provide results of higher quality than the unsupervised ones [1, 9, 14, 26, 27, 33,
34, 37, 42, 53, 56, 64].
This work aims to address the need for both efficient and effective shadow removal in
computer vision workflows, by the following contributions:
• A novel, fully unsupervised shadow removal method, named Simple Unsupervised
Shadow Removal (SUShe), which is based solely on color image features. Unlike pre-
vious methods it is very simple, both in terms of implementation and computational
complexity, whereas it obtains results that are comparable to state-of-the-art deep
learning-based methods.
• A unique shadow segmentation approach efficiently combining a physics-inspired opti-
mization algorithm, superpixel segmentation, and histogram matching, in the context
of a lightweight pre-processing function.
• An extensive experimental study on various publicly available benchmark datasets,
highlighting the tradeoff of efficiency and effectiveness it offers.
The remainder of this paper is organized into six sections. Section2 provides an over-
view of related work, and Section3 details the proposed methodology. Section4 provides
information on the experimental setup and the evaluation framework. Section5 presents
results of the proposed method in comparison with the most relevant state-of-the-art meth-
ods. Section6 provides a perspective in terms of computational complexity. Section7 pro-
vides a discussion of the experimental results, and the main conclusions of this work as
well.
2 Related work
Several shadow detection and removal methods have been based on SMT. This theory
is the foundation for most relighting methods that have been published in the last dec-
ade. Still, it is incomplete, in the sense that it fails to accurately model umbra regions,
to enable correct relighting in the proximity of shadow borders. Apart from the SMT,
several works have been proposed for shadow removal. These include model-based
unsupervised methods, such as the method proposed in [19], where each RGB image
is projected to an 1D invariant direction, in order to recover hues by means of a 2D
chromaticity feature space. In [47], a pyramid-based process is employed for shadow
removal with user assistance. In [36], the main aim was shadow removal in a way that is
robust against texture variations. Later, methods, such as [60], were based on classical
machine learning techniques, which use engineered features, such as texture elements,
and aim to match regions in different lighting conditions [22, 23]. In [12] clustering-
based shadow detection relied on color and texture features, whereas in [41] a shadow
removal method was proposed for images with uniform background. Shadow and lit
regions were separated by ignoring the low-frequency image details. Also, an unsuper-
vised shadow removal method using differential operations for a recent osmosis model
was proposed in [7]. However, most of the afore-mentioned methods have been tested
only in subsets of benchmark datasets. This is because the implementation of these stud-
ies is usually limited to images with specific types of textures and features.
Recently, the focus of research on shadow detection and removal turned to supervised
deep learning-based architectures, such as Convolutional Neural Networks (CNNs), and
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Generative Adversarial Networks (GANs). In [33], a shadow-free image is generated using
two deep networks, SP-Net and M-Net. In [34], a GAN-based framework was trained with
patches extracted from shadow images, following the physics-inspired model of [33]. In
[1], Channel Attention GAN detects and removes shadows by using two networks, which
consider physical shadow properties and equipment parameters. Another network, called
G2R-ShadowNet consists of three subnetworks, and it requires a small number of images
for training [38]. Stacked Conditional Generative Adversarial Network (ST-CGAN) [53]
combines two stacked conditional GANs, which provide generators for the shadow detec-
tion mask and for the shadow-free image. In [20], shadow removal was treated as an image
fusion problem via FusionNet, a network that generates weight maps facilitating the fusion
process. Feature fusion was also employed in [9], integrated with multiple dictionary learn-
ing. During the last years, several studies have also been proposed to increase the effec-
tiveness of shadow removal in the benchmark shadow datasets. In [26] shadow removal
architecture was proposed by Hu etal., aiming to learn direction-aware and spatial char-
acteristics of the images at various levels, using a CNN. Additionally, Hu etal. proposed a
weighted cross entropy loss, to train a neural network for shadow detection. That method
addressed color and luminosity inconsistencies in the training pairs for shadow removal,
by applying a color transfer function. In [62] in order to investigate residual images and
illumination estimation with GANs for shadow removal discrepancies in the training pairs,
a framework named RIS-GAN was proposed. To refine the coarse shadow-removal result
in the shadow-free image of that approach, indirect shadow-removal images were created
by estimating negative residual images and inverse illumination maps, in conjunction with
the coarse shadow-removal image. In [11], the shadow removal problem was approached
in two ways. Firstly, a dual hierarchically aggregation network was proposed to carefully
learn the border artifacts in a shadowed image. Without any down-sampling, a foundation
of dilated convolutions was considered for attention estimation, using multi-context infor-
mation. Secondly, taking into account that training on a small dataset limits the network
ability to recognize textural differences, resulting in color inconsistencies in the shadowed
region, the authors developed a dataset synthesis method based on shadow matting. In [10]
a two-stage context-aware network, called Context-Aware Network (CANet) was proposed
for shadow removal. In CANet the shadow regions receive contextual information from the
corresponding non-shadowed regions. As a next step, encoder-decoder was used to enhance
the results. Mask-ShadowNet was proposed in [24], where a masked adaptive instance
normalization method along with embedded aligners were applied to remove shadows,
considering illumination uniformity and the different feature statistics in the shadow and
non-shadow areas. In [65] a Bidirectional Mapping Network was presented, combining the
learning process of shadow removal and shadow generation into a unified parameter shar-
ing framework. In [51], a style-guided shadow removal network was proposed to address
the issue of visually disharmonic images after shadow removal, and to ensure better image
style coherence. The training of all these deep learning-based methods is associated with a)
a high computational cost, b) non-trivial hardware specifications, and c) a requirement for a
large number of annotated images.
Shadow removal is useful in a variety of computer vision applications, such as the detec-
tion of moving objects and pedestrians, either in indoor or in outdoor environments [29,
31, 63], in navigation-aid systems [44], and the recognition of regions of interest in remote
sensing images [26, 27]. In [49], an automatic shadow mask estimation approach was intro-
duced, aiming to replace manual labeling in a supervised context, using known solar angles
and 3D point clouds. Shadow removal can be an essential component of remote sensing
object detection algorithms, aiming to cope with several challenges, such as the complex
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background, and the variations of scale and density [39, 55]. Wang etal. [54] proposed an
automatic cloud shadow screening mechanism, which was utilized for PlanetScope, a con-
stellation of over 130 satellites of European Space Agency (ESA) that can regularly image
the entire surface of the Earth. In an unsupervised context, a statistical method [3] was pro-
posed for aerial imaging, based on decision trees.
Unlike current, either unsupervised or supervised, shadow removal methods, this work
provides a very simple methodology for automatic shadow removal, based on a novel com-
bination of superpixel segmentation with a strategy for matching shadow and lit regions.
3 Proposed methodology
The proposed methodology is based on a simple, yet very effective strategy. Initially, the
shadow mask is extracted using an evolutionary physics-inspired algorithm. Next, both
shadowed or non-shadowed image regions, which are coherent in terms of texture and
color, are identified and shadow/non-shadow pairs of neighboring superpixels, adjacent to
shadow borders, are determined. The shadowed part of each pair is relighted by means of
histogram matching.
3.1 Shadow detection
Shadow detection refers to the segmentation of a natural image, either in indoor or out-
door settings, in order to extract the shadowed region. Algorithm1 summarizes the shadow
detection stage with a pseudocode, and Fig.2 presents a visual summary of this algorithm.
The Electromagnetism-like Optimization (EMO) [32, 45, 48] algorithm is employed for
multilevel segmentation, aiming to cope with the issue of computational complexity. Ini-
tially, the color space used to represent the input image is converted from RGB to HSV
(line 2). The Hue (H) component of the input image is segmented using the EMO-based
method described in [8], considering that the component Η is invariant to changes in light-
ing. A set of k images hi, i = 1, 2, …, k, is the output of this operation, representing roughly
hue-homogeneous regions (line 3). As a next step, the Value component (V) of the HSV
image is multiplied by each hi, i = 1, 2, …, k, image, resulting in a series of new images
Algorithm1 Shadow Detection Pseudocode
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vi = hi · V, i = 1, 2, …, k, which represent regions with weighted intensities (line 5). This
weighting is performed because the generated image regions have lower intensities in shad-
owed areas. Thus, a subsequent bilevel thresholding step is facilitated. Bi-level threshold-
ing is performed by using EMO, on each of vi, i = 1, 2, …, k, with only one threshold to be
optimized. The result of this operation is a set of k binary images, bi, i = 1,2, …, k (line 6).
In these images, the pixels corresponding to lower intensities (potential shadowed regions)
are set to white, and the remaining pixels are set to black. As a final step, the binary masks
bi, i = 1,2, …, k, obtained for each input image, are aggregated to create a mask B repre-
senting the shadowed regions of the input image (line 7).
3.2 Superpixel matching strategy
Following the application of the shadow detection algorithm, SUShe performs unsu-
pervised shadow removal on image regions with approximately uniform color features.
These regions, which are characterized as superpixels, are obtained using the SLIC
Superpixel segmentation algorithm. Α superpixel matching strategy is then applied
to identify superpixels in the shadow areas that are similar to superpixels in the non-
shadow areas. Relighting is performed by transforming the histogram of the shadow
superpixels, so that it matches the histogram of the respective non-shadow superpixels.
SLIC Superpixel segmentation The Simple Linear Iterative Clustering (SLIC) superpixel
segmentation algorithm performs local clustering of pixels, considering both color and
spatial information, by means of a metric proposed in [2]. The algorithm takes as input an
Fig. 2 Outline of the shadow detection algorithm
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image and the number of superpixels K, in which the input image should be divided. The
initial RGB image is separated into K smaller grid intervals S defined in the xy plane. Each
pixel inside S has spatial coordinates (xi, yi) and color coordinates (Li, ai, bi) in CIE-Lab
color space. Every grid interval S would have a superpixel center Ck = [Lk, ak, bk, xk, yk], for
superpixels that are similar in size. Thus, the following distances are calculated for each
pixel (xi, yi, Li, ai, bi) in S, to the superpixel center Ckusing Eqs. (2) and (3) in order to
define the metric provided in Eq. (4):
where Ds is the final metric, which combines Euclidean distances of the color (in CIE-
Lab) dLab and the Euclidean distances of the spatial coordinates dxy,normalized by the grid
interval S, and m is a variable of the SLIC algorithm, which controls the compactness of
the superpixel. The default value for m was set equal to 10 according to [2]. Each cluster
center Ck is assigned to the best matching pixels from the 2S × 2S area, according to the
distance metric Ds. This process is iterative, until convergence.
SUShe: Simple unsupervised shadow removal The proposed methodology combines two
very simple techniques for region segmentation and relighting of the shadowed areas. The
SLIC Superpixel algorithm is used to segment the input image into many small, approxi-
mately uniform (with respect to color), regions. Algorithm 2 summarizes the shadow
removal stage with pseudocode, and Fig.3 presents a visual summary.
• Initially, the binary shadow mask B (obtained in Subsection3.1) is used to split the
input image I (line 1) into a shadowed regions IS and lit regions IL (line 2). These
regions are obtained by multiplying IS = B · I andIL = (1 − B) · I.
• Next, SLIC superpixel segmentation is applied to IS and IL separately (line 3): IS and
IL are broken down into the shadowed (ISLIC(S)) and the lit image regions ISLIC(L)),with
respect to the color and spatial features of each region.
• The spatial gravity centers of each superpixel
I
SLIC(S)
i
inside the shadow region
GC
shadow
i,i=1, 2 …K
and the corresponding ones of the lit region
GC
litj
,j=1, 2, …K
are calculated (line 4), where Kis the number of superpixels (line 1).
• In each channel of the RGB color space (line 6), for each gravity center
GCshadowi
of
I
SLIC(S)
i
, its Euclidean spatial distance
d
≡d
(
GCshadowi,GClitj
)
from each gravity
center of
GC
lit
j
of superpixel ISLIC(L)j is calculated (line 8) in order to find the minimum one
(line 9). The minimum spatial distance corresponds to the distance of the superpixel that
will illuminate the shadowed superpixel located in the area
GCshadowi
.
• The lit superpixel pairi, that has the minimum distance d from the shadowed one,
I
SLIC(
S
)
i
,
is considered as the optimal counterpart for the respective shadow superpixel.
• Next, the histograms, and the corresponding cumulative distribution functions (cdfs) of the
shadow superpixel
ISLIC(S)i
and of its pairi, are calculated (line 10).
(2)
dLab
=
√(
L
k
−L
i)
2
+
(
a
k
−a
i)
2
+
(
b
k
−b
i)2
(3)
dxy
=
√(
x
k
−x
i)
2
+
(
y
k
−y
i)
2
(4)
D
s=
√
d2
Lab +m2
S
d2
xy
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• Histogram matching [40] is performed on
I
SLIC(S)
i
to transform the shadow histogram, so
that it matches the corresponding lit cdf of pairi. The shadow superpixels are relighted,
using the color values of the lit counterpart pairi (line 11).
• These steps are iteratively performed for all shadow superpixels
I
SLIC(S)
i=1,..K
.
• Finally, all the relighted shadowed superpixels are merged to extract the relighted region
IR(line 12). After completing these iterations, the relighted shadowed region IR is merged
with the initial lit region IL (line 13).
The entire process is repeated three times, for R, G, and B channels, and the results are
concatenated (line 14) to produce the final shadow-free image Inon shadow (line 15).
4 Evaluation
4.1 Experimental setup anddatasets
Τhe proposed methodology and all the experiments have been implemented in MATLAB
R2019a, on an AMD Ryzen Core-75800H 3.2GHz, with 16 GB RAM. The experimen-
tal evaluation has been based on three benchmark datasets, namely the Image Shadow
Algorithm2 Simple Unsupervised Shadow Removal (SUShe) Pseudocode
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Triplets Dataset (ISTD), the Adjusted Image Shadow Triplets Dataset (AISTD), and the
Shadow Removal Dataset (SRD). ISTD is the most challenging shadow dataset employed
in state-of-the-art works. It consists of 2410 triplets, each comprising the initial RGB
images with shadows, the shadow mask, and the ground truth RGB shadow-free image.
ISTD is divided in two subsets; the first subset is composed of 1870 images for training
and the second one contains 540 images for testing. Each image has a size of 480 × 640
pixels. Another well-recognized dataset is AISTD, which is an improved version of the
ISTD, as described in [33], with 1870 training and 540 testing images. Experiments were
also performed using the SRD dataset. This dataset has been proposed in [46] and consists
of 3088 images in total, from which 2680 are used for training and 408 are used for test-
ing. This dataset includes images of various scenes, illumination conditions and object
types, in order to enable the investigation of various shadow and reflectance phenomena.
4.2 Evaluation metrics
The results of the proposed method have been evaluated both quantitatively and qualita-
tively. The quantitative evaluation was based on the Root Mean-Squared Error (RMSE)
and the Peak Signal to Noise Ratio (PSNR). The RMSE between two given images has
been calculated for the shadowed area, the non-shadow area, and for all areas, using the
evaluation code proposed in [21], which has also been used in major state-of-the-art works,
such as [33, 34, 53]. In that code, the RMSE was implemented as follows:
Fig. 3 Illustration of the proposed SUShe shadow removal framework
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where GT is the ground truth image, Outputis the predicted shadow-free image and i = 1, .
. , n represents the index of each pixel in the area of interest (i.e., shadow, non-shadow, all
areas) in the image, and n is the total number of pixels in that area.
The Mean-Squared Error (MSE) between the output of the shadow removal and the
ground truth without shadows is calculated by:
PSNR has been calculated using Eq. (6):
where M is the maximum pixel value in the area of interest. PSNR is measured in deci-
bels (db). A higher PSNR value is linked to higher output image quality (↑). The RMSE
decreases as the output image becomes more similar to the ground truth; therefore, the
output image quality is improved.
Furthermore, we have also assessed our experiments using the novel evaluation metric
Learned Perceptual Image Patch Similarity (LPIPS), which closely matches human recep-
tion [61]. For some predefined network, LPIPS merely computes the similarity between the
activations of two image patches. An image patch perceived similarity is indicated by a low
LPIPS score (↓).
5 Results
In this section, quantitative and qualitative results of the proposed methodology are pre-
sented. Different values of K with respect to superpixel segmentation were tested to find
the most appropriate segmentation level; specifically, K = 70, 80, 90, 100, 400 and 700
superpixels. Tables1, 2 and 3 summarize the results obtained by SUShe in ISTD, AISTD
and SRD datasets, respectively(the best results are indicated in bold). In Table1 it can
be noted that by setting K = 90 (PSNR = 24.82, RMSE = 8.14, LPIPS = 0.079), SUShe
achieves the best shadow removal results in ISTD. Second best results were obtained
(5)
RMSE
=
1
n




n

i=1

GTi−Outputi

2
(6)
MSE
=
1
n
n
∑
i=1
(
GTi−Outputi
)2
(7)
PSNR
=10 log
(
M2
MSE )
Table 1 Quantitative Results of
the proposed methodology for
different superpixel values in
ISTD
ΚPSNR↑RMSE↓LPIPS↓
All regions All regions Shadow Non-shadow All regions
70 24.84 8.15 14.91 6.83 0.078
80 24,77 8.19 15.16 6.83 0.079
90 24.82 8.14 14.87 6.83 0.079
100 24.75 8.17 15.02 6.83 0.080
400 24.71 8.17 14.99 6.83 0.085
700 24.68 8.16 14.99 6.83 0.088
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for K = 70 (PSNR = 24.84, RMSE = 8.15, LPIPS = 0.078). For K = 100, K = 400, K = 700
(mean values approximately equal to PSNR = 24.73, RMSE = 8.17 and LPIPS = 0.084)
the results are comparable. For K = 80 the lowest performance is obtained. In the case
of AISTD (Table2), the best results of SUShe are also obtained for the lowest values
K, in the range tested, i.e. K = 70 (PSNR = 30.09, RMSE = 4.12, LPIPS = 0.076) and
K = 90 (PSNR = 30.06, RMSE = 4.11, LPIPS = 0.076). Again, for larger values of K, i.e.
K = 100, Κ = 400, Κ = 700, the results are comparable to each other (mean values approx-
imately equal to PSNR = 29.60, RMSE = 4.24, LPIPS = 0.083). The results obtained for
K = 70 are the best all over the datasets we have used for evaluation. In the case of SRD,
the optimal results obtained for K = 70 lead to the lowest RMSE score (PSNR = 22.05,
RMSE = 8.68, LPIPS = 0.167) The values K = 80, 90 lead to slightly inferior accuracy. It
can be observed that higher values for K are not linked with higher quality results.
Figure4 indicates that the proposed methodology is relatively insensitive to K. Espe-
cially in terms of LPIPS, the results are comparable using different values of K. Yet, its
performance is slightly better for the lowest values of K, in the range tested.
Tables 4, 5 and 6 present experimental comparisons between SUShe (indicated in
bold)and state-of-the-art shadow removal algorithms. The results presented for the latter
are derived from the literature. RMSE is computed in three ways: a) inside the shadowed
region (Shadow), outside the shadowed region (Non-shadow) and in the entire image (All
regions). Figures5, 6 and 7 illustrate qualitative results of SUShe and other state-of-the-art
algorithms, including all unsupervised methods and some of the supervised ones, which
are publicly available by the authors.
Table 4 presents comparisons on ISTD. SUShe outperforms all non-neural net-
work-based methods ([21, 23, 58]), as it achieves the best results in terms of all met-
rics (PSNR = 24.82, RMSE = 8.14, LPIPS = 0.079). The methods of Guo et al. [23]
and Gong etal. [21] have been created using supervised techniques in the context of
Table 2 Quantitative Results of
the proposed methodology for
different superpixel values in
AISTD
ΚPSNR↑RMSE↓LPIPS↓
All regions All regions Shadow Non-shadow All regions
70 30.09 4.12 12.26 2.53 0.076
80 29.99 4.14 12.43 2.53 0.076
90 30.06 4.11 12.22 2.53 0.076
100 29.91 4.14 12.40 2.53 0.077
400 29.51 4.24 13.03 2.53 0.083
700 29.24 4.34 13.59 2.53 0.086
Table 3 Quantitative results of
the proposed methodology for
different superpixel values in
SRD
ΚPSNR↑RMSE↓LPIPS↓
All regions All regions Shadow Non-shadow All regions
70 22.05 8.68 16.31 7.25 0.167
80 21.95 9.69 23.25 4.54 0.168
90 21.91 9.66 23.16 4.54 0.168
100 21.85 9.74 23.44 4.54 0.168
400 21.03 10.56 26.41 4.54 0.168
700 20.64 10.94 27.81 4.54 0.178
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shadow detection and removal. On one hand, Guo etal. use pairwise classification for
shadow removal. On the other hand, the method of Gong etal. requires indication of the
shadowed and lit areas using a GUI tool to apply shadow detection. In addition, SUShe
outperforms three state-of-the-art neural network-based methods: ARGAN [14], Cycle-
GAN [64], the method proposed by Nagae etal. [43], and the well-known SP + M Net,
DHAN [33] (Table4). The rest of the neural network-based methods achieve RMSE
values that are lower than the RMSE of SUShe. Still, SUShe obtains LPIPS = 0.079
in the ISTD, which is the lowest value with the exception of ST-CGAN. Approaches
such as [26, 27, 33, 37, 46], [20, 30] lead to results comparable to SUShe (with a dif-
ference in RMSE that is not exceeding 2.0); however, these approaches require training.
Figure5 illustrates indicative shadow removal results of SUShe and the state-of-the-art
Fig. 4 LPIPS sensitivity for different K values (a) in ISTD, (b) in AISTD and (c) in SRD
Table 4 Quantitative results in comparison with other state-of-the-art methodologies for ISTD
N/A: Not Applicable.
Methodology Training PSNR↑RMSE↓LPIPS↓
All regions All regions Shadow Non-shadow All regions
Yang etal. (2012) [58] N/A 20.11 15.63 19.82 14.83 –
Guo etal. (2013) [23] N/A 22.33 9.30 18.95 7.46 –
Gong etal. (2016) [21] N/A 24.07 8.53 14.98 7.29 –
ARGAN (2019) [14] paired 24.25 11.02 15.49 10.21 –
ST-CGAN (2018) [53] paired 24.85 7.47 10.33 6.93 0.067
DSC (2020) [26] paired 26.62 6.67 9.76 6.93 0.202
DeshadowNet (2017) [46] paired 24.25 7.60 – – –
Fu etal. (2021) [20] paired 27.19 5.92 7.77 5.56 0.086
SP + M-Net (2019) [33] paired 24.10 8.32 11.22 7.77 0.080
Nagae etal. (2020) [43] paired 24.87 10.63 17.80 8.62 –
DHAN (2020) [11] paired 27.88 8.46 10.56 7.84 –
Cycle-GAN (2017) [27, 64] unpaired – 8.16 – – 0.120
Mask-ShadowGAN(2019) [27] unpaired 25.07 7.41 12.67 6.68 0.250
LG-ShadowNet (2021) [37] unpaired 25.92 6.67 10.93 5.94 –
DC-ShadowNet (2021) [30] unpaired 22.94 6.57 10.64 5.80 0.090
SUShe N/A 24.82 8.14 14.87 6.83 0.079
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methods compared. As can be observed in Fig.8b or e, some methods completely alter
the image, while others fail in completely removing the shadow (Fig.8c, d, f, j). In addi-
tion, in Fig.8h, the pair of shadowed/non-shadowed regions is erroneous, leading to a
relighting from an erroneous non-shadow area and eventually to an erroneous bright-
ness reset. SUShe is the only completely unsupervised methodology with a satisfactory
performance along the entire ISTD. The comparative results in the ISTD are graphically
represented in Fig.5.
Table5 presents comparisons between SUShe and state-of-the-art shadow removal
methods, for AISTD. In this case, SUShe is ranked second with respect to PSNR and
Table 5 Quantitative results in comparison with other state-of-the-art methodologies for AISTD
Methodology Training PSNR↑RMSE↓LPIPS↓
All regions All regions Shadow Non-shadow All regions
Yang etal. (2012) [58] N/A 19.77 16.00 24.70 14.40 –
Guo etal. (2013) [23] N/A 24.27 6.10 22.00 3.10 –
Gong etal. (2016) [21] N/A 27.78 5.10 14.42 3.39 0.086
ST-CGAN (2018) [53] paired 23.14 8.70 13.40 7.70 0.150
DeshadowNet (2017) [46] paired – 7.60 15.90 6.00 –
SG-ShadowNet (2022) [51] paired 32.45 3.40 5.90 3.40 0.070
Fu etal. (2021) [20] paired 29.44 3.80 6.50 4.20 0.106
SP + M-Net (2019) [33] paired 30.02 4.41 8.84 3.64 0.085
Nagae etal. (2020) [43] paired 26.73 9.40 17.11 6.54 –
DHAN (2020) [11] paired 24.86 10.05 12.09 9.42 –
Mask-ShadowGAN(2019) [27] unpaired 26.89 5.30 12.50 4.00 0.095
LG-ShadowNet (2021) [37] unpaired 29.22 5.00 10.60 5.00 0.103
DC-ShadowNet (2021) [30] unpaired 28.76 4.60 10.30 3.50 0.170
SUShe N/A 30.06 4.11 12.22 2.53 0.076
Table 6 Quantitative results in comparison with other state-of-the-art methodologies for SRD
Methodology Training PSNR↑RMSE↓LPIPS↓
All regions All regions All regions
Yang etal. (2012) [58] N/A – 22.57 –
Guo etal. (2013) [23] N/A – 12.60 –
Gong etal. (2016) [21] N/A – 8.73 –
DSC (2020) [26] paired 21.52 6.21 0.147
DeshadowNet (2017) [46] paired – 6.64 0.165
SG-ShadowNet (2022) [51] paired 31.16 6.23 0.099
Fu etal. (2021) [20] paired 27.74 6.51 0.153
Nagae etal. (2020) [43] paired 22.15 15.59 –
DHAN (2020) [11] paired 27.66 8.68 –
Cycle-GAN (2017) [64] unpaired – 9.14 –
Mask-ShadowGAN (2019) [27] unpaired – 7.32 –
DC-ShadowNet (2021) [30] unpaired 30.55 4.66 0.167
SUShe N/A 22.05 8.68 0.167
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LPIPS, after SP + M Net and SG-ShadowNet, and is ranked third with respect to RMSE.
The difference between SUShe results and these methods is notably small, given the
higher computational complexity of the latter. Figure9 illustrates comparative results
on images from AISTD. Once again, the methods proposed by Guo etal., Gong etal.,
and the methods DC-ShadowNet and LG-ShadowNet (Fig.9c-e, h) fail to remove the
shadow in the second and third image (center and right column), whereas the method
of Yang etal. (Fig.9b) alters the image inside and outside the shadow regions. The best
results are obtained by SUShe, whereas comparable results are obtained by SG-Shad-
owNet, DHAN, and by the method of Fu etal. (Fig.9f-g, i). The comparative results in
the AISTD are also graphically represented in Fig.6.
Fig. 5 Comparative results on the ISTD (from Table4), in terms of RMSE, PSNR, and LPIPS metrics. The
horizontal lines represent the mean scores obtained from all the previously proposed methods per metric
Fig. 6 Comparative results on the AISTD (from Table5), in terms of RMSE, PSNR, and LPIPS metrics.
The horizontal lines represent the mean scores obtained from all the previously proposed methods per
metric
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Table 6 presents comparisons on SRD. In this case, SUShe outperforms all unsuper-
vised methods, and notably outperforms Cycle-GAN and the method of Nagae etal. as
well. Furthermore, the performance of SUShe is comparable to the performances of
DHAN (RMSE = 8.68) and DeShadowNet [46], in terms of LPIPS. Figure 10 illustrates
indicative qualitative results of SUShe and other state-of-the-art algorithms on images
from SRD, including the supervised methods. In the case of the first image of Fig.10 (left),
the output of SUShe is obviously closer to the ground truth than the rest of the methods. In
the case of the second image of Fig.10 (right), the result of SUShe is comparable to that
of DeshadowNet and ARGAN, DSC, DC-ShadowNet, Fu etal., and SG-ShadowNet. It is
also worth noting that SUShe preserves the details of the original image, unlike ST-CGAN,
which introduces blur artifacts on the original image. Overall, SUShe achieves compara-
ble shadow removal results with some supervised methods. The comparative results in the
SRD are also graphically represented in Fig.7.
6 Computational complexity
The computational complexity of SUShe is estimated in order to quantitatively assess its
efficiency. More specifically:
a) SLIC Superpixels are used for segmentation of both lit and shadowed regions by
employing hue and spatial coordinates. SLIC bypasses tens of thousands of point-to-point
redundant distance calculations by localizing the search in the clustering process. SLIC is
O(N), where N is the number of the pixels of an image [2].
b) For each RGB channel (c = 3 for the loops in the following process):
• Histogram calculation of an image is O(N), since N =width × height.
• Calculation of the gravity centers of the lit superpixels is O(K), where Kis the number
of lit superpixels.
• Scanning the shadow superpixels to calculate the following features, is O(K):
Fig. 7 Comparative results on the SRD (from Table6), in terms of RMSE, PSNR, and LPIPS metrics. The
horizontal lines represent the mean scores obtained from all the previously proposed methods per metric
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(a)
Shadow Image
(b)
Yang et al., (2012)
(c)
Guo et al., (2012)
(d)
Gong et al., (2016)
(e)
STCGAN, (2018)
(f)
DSC (2020)
(g)
SP+M Net (2019)
(h)
DC-ShadowNet (2
021)
(i)
Fu et al., (2021)
(j)
LG-ShadowNet, (202
1)
(k)
DHAN, (2020)
(l)
Ground Truth Image
(m)
SUShe
Fig. 8 Indicative results of SUShe and other state-of-the-art methods in ISTD. a Shadow Image, b Yang
etal., (2012)[58], c Guo etal., (2012)[23], d Gong etal., (2016)[21], e STCGAN, (2018)[53], f DSC (2020)
[26], g SP + M Net (2019)[33], h DC-ShadowNet (2021)[30], i Fu etal., (2021)[20], j LG-ShadowNet,
(2021)[37], k DHAN, (2020)[11], l Ground Truth Image, m SUShe
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(a)
Shadow Image
(b)
Yang et al., (2012)
(c)
Guo et al., (2012)
(d)
Gong et al., (2016)
(e)
DC-ShadowNet, (2021)
(f)
Fu et al., (2021)
(g)
SG-ShadowNet, (2022)
(h)
LG-ShadowNet, (2021)
(i)
DHAN, (2020)
(i)
Ground Truth Image
(j)
SUShe
Fig. 9 Indicative results of SUShe and other state-of-the-art methods in AISTD, (a) Shadow Image, (b)
Yang etal., (2012)[58], (c) Guo etal., (2012)[23], (d) Gong etal., (2016)[21], (e) DC-ShadowNet, (2021)
[30], (f) Fu etal., (2021)[20], (g) SG-ShadowNet, (2022)[51], (h) LG-ShadowNet, (2021)[37], (i) DHAN,
(2020)[11], (i) Ground Truth Image, (j) SUShe
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(a)
Shadow Image
(b)
DeshadowNet, (2017)
(c)
STCGAN, (2018)
(d)
ARGAN, (2019)
(e)
DSC, (2020)
(f)
DC-ShadowNet, (2021)
(g)
Fu et al., (2021)
(h)
SG-ShadowNet. (2022)
(i)
DHAN, (2020)
(j)
Ground Truth Image
(k)
SUShe
Fig. 10 Indicative results of SUShe and other state-of-the-art methods in SRD. a Shadow Image, b DeshadowNet,
(2017)[46], c STCGAN, (2018)[53], d ARGAN, (2019)[14], e DSC, (2020)[26], f DC-ShadowNet, (2021)[30], g
Fu etal., (2021)[20], h SG-ShadowNet. (2022)[51], i DHAN, (2020)[11], j Ground Truth Image, k SUSh
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• Calculation of the Euclidean distance with all lit superpixels and finding the minimum
amounts to O(K).
• Thecalculationof cdfsis estimated almost equal to O(N).
Histogram matching amounts to O(greylevels2).
A quantitative comparison of the Floating-point Operations per Second (FLOPS)
between SUShe and available deep learning-based methods is presented in Table 7 and
Fig.11. It can be noticed that SUShe has a significantly lower FLOPS value (indicated in
bold).
7 Discussion andconclusions
This work investigated a simple, efficient and effective solution for the complex prob-
lem of shadow removal, which can affect object detection and recognition algorithms,
deteriorating their performance. The experimental results showed that by combin-
ing simple segmentation and color enhancement algorithms, the original brightness
of shadowed regions can be restored. This was validated by quantitative and qualita-
tive comparisons performed with both unsupervised and supervised state-of-the-art
methods. All experiments were performed in three widely adopted publicly available
Table 7 The number of FLOPS
per image for different shadow
removal methods
Method FLOPS×109
Mask-ShadowGAN 266.4
Fu etal. 104.8
LG-ShadowNet 82.7
SP + M-Net 39.8
SG-ShadowNet 39.7
SUShe 0.7
Fig. 11 The number of FLOPS
per image (from Table7) for dif-
ferent shadow removal methods
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benchmark datasets. From Tables4, 5 and 6 and Figs. 5, 6 and 7, it is evident that
SUShe outperforms all state-of-the-art unsupervised methods compared, as well as
some supervised ones (Cycle-GAN, ARGAN, Nagae etal., DHAN, LG-ShadowNet,
DC-ShadowNet). As for those that SUShe does notoutperform, such as SG-Shad-
owNet, the results of SUShe are comparable both quantitatively and qualitatively
(Figs. 8, 9 and 10). To the best of our knowledge SUShe is the only unsupervised
algorithm which provides a similar shadow removal performance with most of the
state-of-the-art supervised methods compared, on the full, widely used benchmark
datasets considered in this study. Furthermore, the comparisons with state-of-the-art
deep-learning-based methods in terms computational complexity showed that SUShe
is much more efficient (Table7 and Fig.11).
Overall, the following conclusions can be derived:
• SUShe is very simple to implement and of low computational complexity.
• Its computational complexity is generally lower than that of the state-of-the-art algo-
rithms for shadow removal.
• The results obtained indicate that SUShe can remove shadows better than any of the
compared state-of-the-art unsupervised shadow removal methods.
• In comparison with the supervised state-of-the-art shadow removal methods, its per-
formance is comparable or better.
• Solving the shadow removal problem does not necessarily require complex deep
learning-based solutions.
Shadow removal is instrumental for object recognition in various domains such as
remote sensing image processing, traffic monitoring and object recognition. Future work
will involve evaluation of SUShe in various applications where rapid system response
is required, such as assistive navigation systems [13]. Furthermore, SUShe can be also
applied in the medical domain to investigate how shadow removal can optimize the results
of medical imaging in the shadowed regions of an internal body organ, e.g., the shadowed
regions in images obtained from gastrointestinal capsules, diagnostic ultrasounds etc.
Acknowledgements The authors would like to thank Prof. Yandong Tang for the SRD dataset provision.
This work was co-financed by Greece and the European Union (European Social Fund-ESF) through the
Operational Programme «Human Resources Development, Education and Lifelong Learning» in the context
of the Act “Enhancing Human Resources Research Potential by undertaking a Doctoral Research” Sub-
action 2: IKY Scholarship Programme for PhD candidates in the Greek Universities.
Funding Open access funding provided by HEAL-Link Greece.
Data availability All data analyzed during this study are available in https:// github. com/ DeepI nsight-
PCALab/ ST- CGAN (ISTD) and https:// github. com/ cvlab- stony brook/ SID (AISTD), and included in this
published article [46] (SRD).
Declarations
Conflict of interest The authors declare that they have no conflict of interest.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License,
which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long
as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Com-
mons licence, and indicate if changes were made. The images or other third party material in this article
are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the
material. If material is not included in the article’s Creative Commons licence and your intended use is not
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permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly
from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.
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