HaJeong-Won1
KimJong-Ok1
-
(School of Electrical Engineering, Korea University / 145 Anam-ro, Seongbuk-gu, 02841,
Korea
{jwon9339, jokim}@korea.ac.kr
)
Copyright © The Institute of Electronics and Information Engineers(IEIE)
Keywords
Color constancy, Review, Spatial, Temporal, Statistics-based, Alternative current
1. Introduction
Color constancy is the ability to recognize the inherent color invariant of the illuminant.
Although the human visual system has color constancy ability, the images captured
with a digital camera is affected by the illuminant. Therefore, estimating and eliminating
illuminants essential in the image signal processing pipeline. This process affects
not only the visual quality, but also the performance of computer vision tasks, such
as classification and segmentation [1]. Because a white balance is one of the important processes in the image signal processing
pipeline, it has been studied for a long time. Fig. 1 presents the concept of color constancy. The goal of color constancy is to correct
the image captured under colored illuminant to white light. This paper provides a
comprehensive review of color constancy methods. Table 1 lists the color constancy methods introduced in this paper.
Conventional color constancy methods can be classified as statistics-, physics-, and
learning-based. Statistics-based algorithms formulate the hypothesis that can be applied
to natural scenes and exploit it for illuminant estimations. Although it has been
used widely for commercial devices, it has limitations for uniformly colored regions
with narrow color distributions. The physics-based methods use physical models with
respect to the surface reflection of light. It is highly challenging to accurately
determine the model parameters of the ill-posed problem formulated by the physics
model accurately is highly challenging. Owing to the development of deep learning,
it has been exploited for illuminant estimation and contributed to performance improvement.
With the development of imaging technologies, high-speed cameras have been equipped
with consumer devices. The high-speed camera can capture rapid changes and variations
of scenes imperceptible to the human eyes. With the utility of high-speed cameras,
it is expected that they will be used popularly for consumer devices, such as smartphones.
Most color constancy studies have exploited a single image, and several works are
using temporal features of multiple frames. Recently, some studies exploited the temporal
features of AC light sources in illuminant estimation. Fig. 2 shows the scenario of
illuminant estimation under AC light sources. The intensity of light sources varies
with time because light sources are supplied by the alternative current (AC) power.
It flickers with double AC frequency. Although human eyes cannot capture this fast
variation, it can be observed with a high-speed camera whose capturing speed is faster
than the fluctuation. This temporal fluctuation can be a powerful prior to illuminant
estimation. Several studies have exploited AC fluctuations for color constancy [14-18]. [14] first proposed exploiting AC fluctuation for illuminant estimation. It selects AC
pixels that follow sinusoidal curves and exploited dichromatic plane estimation. [16] proposed a temporal gradient map generated with the intensity difference between
adjacent frames. They assumed that the more illuminated region showed higher variations.
In reference [15], all the parameters of the dichromatic model were estimated with temporal priors
where the reflection components fluctuate sinusoidally. [17,18] extracted the temporal correlation of high-speed video with a non-local neural network.
The temporal correlation map was used for temporal feature extraction. With the temporal
fluctuation of AC light bulbs, [14-18] achieved more accurate illuminant estimation than the spatial-based methods.
There are various color constancy datasets for single image methods, such as Gehler-Shi
Color Checker [20] and NUS [21]. On the other hand, the temporal color constancy methods assume AC variations of
illuminant, and conventional datasets were unsuitable for evaluation. Therefore, the
high-speed video dataset [15] was proposed and exploited for experiments. The high-speed video dataset consists
of various objects and illuminant conditions, such as practical indoor scenes and
laboratory environments.
This paper introduces various color constancy methods that exploit spatial and temporal
features. The remainder of the paper is organized as follows. Section 2 describes
the color constancy methods that exploit only spatial features. Section 3 summarizes
the temporal color constancy methods. Experimental results are shown in Section 4.
Finally, Section 5 concludes the paper.
Fig. 1. Concept of color constancy.
Table 1. Summary of color constancy methods.
|
Methods
|
Input
|
Statistics
|
Gray world [2], Max-RGB [3], Shades of gray [4], 1st order grey edge [5], 2nd order grey edge [5], Grey pixels [6]
|
Single image
|
Physics
|
Spatial
|
IIC [7], ICC[8]
|
Single image
|
Temporal
|
Prinet et al. [13], Yoo et al. [14]
|
High-speed video
|
Learning
|
Spatial
|
Bianco et al. [9] , FFCC [19], FC4 [10], ReWU [11]
|
Single image
|
Temporal
|
Ha et al. [16], DDME [15], Yoo et al. [17], Yoo et al. [18]
|
High-speed video
|
2. Spatial Color Constancy
The image value $f$ depends on the spectral curve of light source $e\left(\lambda
\right)$, surface reflectance $s\left(\lambda \right)$, and camera sensitivity function
$c\left(\lambda \right)$:
where $\lambda $ and $w$ mean wavelength and visible spectrum, respectively. It is
assumed that the color of the illuminant is uniform in the scene. The illuminant that
is estimated in color constancy can be expressed as follows:
To correct the color-biased image with an estimated illuminant, normalized light source
color is used. The normalized illuminant vector $\hat{e}$ is exploited because the
goal of correction is to change the color of the scene, not the brightness. The corrected
pixel can be obtained as follows:
The following describes spatial color constancy methods, which are divided into statistics-,
physics-, and learning-based.
2.1 Statistics-based Methods
The statistics-based methods exploit the statistical properties of a scene. The best-known
assumption of the statistics-based approach is the gray world [2]. It assumes that the average reflectance of a scene under white illuminant is achromatic.
The illuminant color is estimated with the average of the image.
where $k$ is a multiplicative constant and $e$ is a normalized illuminant vector.
Another assumption [3] is that there is a patch with perfect reflectance in a natural image. Because this
patch shows high reflectance in the scene, the max value of each channel represents
the illuminant.
[4] introduces the gray world and max-RGB algorithms as exceptional cases of more general
color constancy algorithms based on the Minkowski norm as follows:
The gray world and max-RGB are the same as $p=1$ and $p=~ \infty $, respectively.
[4] reported this as shades of gray and found that the best results are obtained with
$p=6$.
[5] assumed that the derivative of an image is achromatic, and it is called the gray
edge. The illuminant can be estimated with the 1$^{\mathrm{st}}$ and 2$^{\mathrm{nd}}$
derivatives of an image. It generalized gray-world, max-RGB, and shades of gray and
proposed a gray edge algorithm as follows:
Because the average reflectance of achromatic objects under colored illuminant is
identical to illuminant chromaticity, [6] assumed that gray pixels exist in natural scenes. [6] defined an illuminant invariant measure to find gray pixels in a color-biased image.
The illuminant can be estimated with the average of selected pixels that are close
to gray.
2.2 Physics-based Methods
The physics-based methods exploit the physical interaction between the object and
the light source. They are based on the dichromatic model:
where$~ \Lambda _{c}$ and $\Gamma _{c}$ are diffuse and specular chromaticity, respectively,
and $m_{d}$ and $m_{s}$ are their respective weights. Specular chromaticity is identical
to the illuminant color, while diffuse reflection represents the intrinsic color of
objects.
In the inverse intensity chromaticity space [7], the linear relationship between RGB chromaticity ($\sigma _{c}=\frac{I_{c}}{\sum
I_{i}}$) and inverse intensity was studied and is expressed as follows:
where $p_{l}=m_{d}\left(\Lambda _{c}-\Gamma _{c}\right)$. Based on [7], Woo et al. [8] exploited selected specular pixels for accurate specular chromaticity estimation.
[8] studied the relationship between the length of the dichromatic line and specularity.
It obtained a reliable dichromatic line using pixels that are colored uniformly, bright
as possible, and produced a long line segment in chromaticity space.
2.3 Learning-based Methods
The learning-based model estimates the illuminant by learning the features from the
training dataset. [9] first introduced CNN in color constancy. It extracts the features with CNN, and the
reshaped features were fed into fully connected layers, and a three-dimensional illuminant
vector was estimated. On the other hand, the network accepts the patch of a given
image. If a patch with less illuminant information is selected, it may affect performance.
To alleviate this problem, FC4 [10] estimates illuminant with a full image. It generates a four-channel output, a local
illuminant map (three channels), and a confidence map (1 channel). A local illuminant
map represents the illuminant of a local region, and confidence means the estimated
accuracy of the local illuminant at the corresponding region. The global illuminant
was finally estimated using the weighted sum of local illuminants using a confidence
map.
Instead of extracting deep features with CNN, [11] reported that color constancy can be solved at a more lightweight model. Conventional
algorithms use some pixels more important for illuminant estimation, and they detect
and analyze these pixels. As the conventional methods, [11] proposed a feature map reweight unit that can focus on significant pixels.
3. Temporal Color Constancy
Some studies exploit the temporal features of image sequences. Yang et al. [12] assumed fixed objects and moving cameras under constant illuminant chromaticity.
Different images (I and J) captured with different viewing points are used. Let a
pixel $p$ in I correspond to $\overline{p}$ in J. Then, the pixel value $I\left(p\right)$
and $J\left(\overline{p}\right)$ share diffuse components, and the difference comes
from specular components. The normalized difference of matching pixels indicates the
illuminant chromaticity:
Prinet et al. [13] enhanced Yang et al. [12] by formulating it in a probabilistic manner and achieved a robust illuminant estimation
performance.
Several studies assumed high-speed video captured under AC light sources. Yoo et al.
[14] proposed using AC variation of light sources in illuminant estimation. Previous methods
[12,13] need to find corresponding pixels between frames. On the other hand, in the AC light-based
method, it is easier to find corresponding pixels of adjacent frames because of high-speed
capture. The intensity of light sources supplied by alternative current fluctuates
sinusoidally over time. This temporal fluctuation is captured with a high-speed camera
and is exploited to select AC pixels. An AC pixel is a pixel whose intensity varies
sinusoidally due to AC variation of light sources. The mean intensity of RGB channels
($I_{m}=\left(I_{R}+I_{G}+I_{B}\right)/3$) can be modeled as a sinusoidal curve. It
is represented as follows:
$A_{m}$ is the amplitude; $f_{ac}$ is the standard frequency of the AC current (typically
50 or 60 Hz); $f_{cam}$ is the frame rate; $off$ is the offset value. The parameter
set $\Theta =\left(A_{m},~ \phi ,~ off\right)$ was estimated iteratively using the
Gauss-Newton method. Fig. 3 shows the modeling result of the intensity variation of the boxed regions with a
sinusoidal curve. The illuminant is estimated with the intersection of multiple dichromatic
planes of AC pixels. Because of the short exposure time of the high-speed image, it
contains inherent low-light noise, and it makes dichromatic model estimation challenging.
The noisy pixels can be removed, and an accurate dichromatic model can be estimated
by selecting AC pixels.
DDME
[15] estimates all parameters ($m_{d},~ \Lambda ,~ m_{s}$, and $\Gamma $) of the dichromatic
model with temporal features of high-speed video. The image pixels can be factorized
to chromaticity dictionary matrix $D$ and coefficient matrix $C$ as follows:
$D$ contains the illuminant and diffuse chromaticity dictionary, and $C$ represents
the weight coefficient $m_{d}$ and $m_{s}$. The proposed network consists of two branches,
and the chromaticity dictionary and coefficient are estimated with each branch. Although
the estimation of the dichromatic model is a highly ill-posed problem, [15] successfully estimated the parameters with temporal priors of a high-speed video.
The chromaticity of diffuse reflection between adjacent frames is approximately identical
because the camera and object are static in a short interval. As the intensity of
the AC light source varies, the intensities of the reflection components (diffuse
and specular) also vary sinusoidally. Therefore, $m_{d}$ and $m_{s}$ are regularized
to have sinusoidal variation. The mean coefficient weights were fitted with Gauss-Newton
method, as reported elsewhere [14]. The regression error is reflected as a loss function. With these temporal constraints,
the network of [15] accurately learns the parameters of the dichromatic model. Color constancy and highlight
removal can be conducted successfully using the estimated dichromatic model.
Ha et al. [16] proposed using the temporal gradient of high-speed video in illuminant chromaticity
estimation. The proposed network comprises two subnets that estimate local illuminant
and confidence map. The local illuminant and confidence map means the local illuminant
of each local region and the estimated accuracy of the corresponding region, respectively.
[16] assumed that highly illuminated regions show high-intensity variation. It calculates
the temporal gradient of the video with the intensity difference between two adjacent
gray frames. The maximum operation is taken among temporal gradient frames. Fig. 4 shows the generation process of the maximum gradient map. The maximum gradient map
is used to estimate the confidence map. The confidence map can detect the highly illuminated
region useful for illuminant estimation. The accurate estimation is achieved by estimating
illuminants with highly illuminated regions.
[17,18] estimated the illuminant by extracting a temporal correlation map of high-speed video.
The temporal correlation of high-speed video was extracted with a non-local block.
The network of [17] consisted of temporal and spatial branches. The temporal branch uses temporal correlation
weighted input frames as input. Fig. 5 presents the extraction of temporal features with a non-local neural network [22]. The temporally attentive regions can be detected using the temporal features. By
weighting the input frames with temporal correlation map, the illuminant map that
contains AC variation information can be obtained. As reported elsewhere [14], detecting AC-illuminated regions contributes to illuminant estimation. The spatial
branch learns spatial features of a single image as the spatial-based color constancy
deep networks. [17] improved the illuminant estimation performance by adding a spatial branch in the
previous study [18]. [17] claimed that the temporal features can contribute to illuminant estimation of complex
indoor scenes, while spatial features are for simple laboratory scenes.
Fig. 3. AC variation modeling of high-speed video.
Fig. 4. Generation of maximum gradient map. Reprinted from [16]. Copyright by IEEE.
Fig. 5. Temporal feature extraction based on the non-local neural method. Reprinted from [17]. Copyright by IEEE.
4. Experimental Results
4.1 Dataset
There are several public datasets for single-image color constancy, such as Gehler-Shi
Color Checker [20] and NUS [21]. On the other hand, these datasets are unavailable for temporal color constancy methods
that require multiple frames as input. Using high-speed video with temporal AC variation
was first conducted in [14], and a high-speed dataset was constructed. It contains 80 high-speed raw videos captured
with Sentech STC-MCS43U3V high-speed vision camera. It includes various objects like
plastic, rubber, metal, stones, and fruit. The raw frames were normalized and demosaicked
to estimate illuminant and white balance. A color checker was captured for the ground
truth illuminant. The dataset was captured in a laboratory setting that blocks external
lights.
[15] extended the high-speed dataset of [14] to contain diverse scenes. It comprised 225 raw high-speed videos captured with Sentech
STC-MCS43U3V high-speed vision camera. The camera was set to a frame rate of 150 FPS
and an exposure time of 1/300 sec. Total 225 scenes were captured and divided into
150 and 75 scenes for training and test, respectively. Although the previous dataset
[14] only contained closed scenes, [15] contained open indoor scenes for practical performance evaluation. The former scenes
occupied 33.3%, and 66.7% were open scenes. Fig. 6 shows sample images of the dataset. Two types of light sources (incandescent and
fluorescent) were used to capture the closed scenes. The open scenes are captured
in indoor public places, such as caf\'{e}s, libraries, schools, and hotels. These
scenes may include ambient light or sunlight, which is a practical environment of
the real world. The color checker was captured for ground truth illuminant.
Fig. 6. Sample images of the high-speed dataset [15]. It consists of closed (top row) and open (bottom) environment.
4.2 Experimental Results
The angular error, which is a common quality measure of color constancy, was used
for the performance evaluation. The direction of the illuminant vector indicates the
illuminant color and the intensity is not considered. The angular error between the
ground truth ($\Gamma _{gt}$) and estimated illuminant ($\Gamma _{est}$) was calculated
as follows:
A smaller angular error indicates a more accurate estimation.
Table 2 lists the angular error of various color constancy methods. The color constancy methods
are categorized as statistics, physics, and learning-based. In addition, the methods
are divided into temporal and spatial approaches by whether they use temporal features.
The high-speed dataset [15] is used to evaluate the performance of temporal methods. Note that all the learning-based
methods are trained with the high-speed dataset. For a fair comparison, the angular
errors of the single image-based methods are averaged for five frames.
As shown in Table 2, the temporal methods performed better than the spatial ones. To confirm the robust
performance, the average angular error for closed and ambient scenes are shown in
Table 2. [14] reported the best performance for closed scenes between physics-based methods. On
the other hand, it failed to find AC pixels under complex illuminant environments
or weak temporal variation and provided the worst estimation for ambient scenes among
physics-based methods. With deep learning methods, the illuminant estimation performance
was highly improved. Fig. 7 presents the white-balanced versions of the estimated illuminants with the learning-based
methods. The temporal-based methods achieved better reconstruction than the spatial-based
methods. Also ,the temporal feature methods showed performance improvement for ambient
scenes. It means that the temporal methods are robust to illuminant environments.
With temporal features of AC light source, the robust performance can be achieved.
Fig. 7. (a) Input image, and white-balance image with (b) ground truth illuminant and estimated illuminant with (c) Bianco et al. [9]; (d) FFCC [19]; (e) FC4 [10]; (f) ReWU [11]; (g) Ha et al. [16]; (h) DME [15]; (i) Yoo et al. [17].
Table 2. Angular Error Comparisons.
Method
|
Mean
|
Median
|
Best-25%
|
Worst-25%
|
Closed
|
Ambient
|
Statistics
|
Gray world [2]
|
4.08
|
3.42
|
1.27
|
8.34
|
6.28
|
2.97
|
Max-RGB [3]
|
13.22
|
13.62
|
5.92
|
20.65
|
14.85
|
12.40
|
Shades of gray [4]
|
5.56
|
4.40
|
1.40
|
12.61
|
5.65
|
5.12
|
1st order grey edge [5]
|
10.34
|
9.94
|
2.69
|
18.84
|
7.72
|
11.65
|
2nd order grey edge [5]
|
12.39
|
12.12
|
3.65
|
22.06
|
9.59
|
13.79
|
Grey pixels [6]
|
8.17
|
6.41
|
1.79
|
17.88
|
7.19
|
8.65
|
Physics
|
Spatial
|
IIC [7]
|
4.25
|
3.28
|
1.03
|
9.08
|
3.94
|
4.41
|
ICC[8]
|
3.47
|
2.72
|
1.10
|
7.53
|
5.17
|
2.61
|
Temporal
|
Prinet et al. [13]
|
5.30
|
3.95
|
0.92
|
11.70
|
7.83
|
4.03
|
Yoo et al. [14]
|
4.60
|
3.75
|
1.59
|
8.91
|
3.65
|
5.07
|
Learning
|
Spatial
|
Bianco et al. [9]
|
1.79
|
1.12
|
0.36
|
4.42
|
1.44
|
1.97
|
FFCC [19]
|
1.42
|
0.68
|
0.12
|
4.18
|
0.19
|
2.04
|
FC4 [10]
|
2.26
|
2.05
|
0.76
|
4.17
|
2.30
|
2.25
|
ReWU [11]
|
1.26
|
0.55
|
0.30
|
3.30
|
0.87
|
1.46
|
Temporal
|
Ha et al. [16]
|
0.95
|
0.24
|
0.12
|
2.84
|
0.35
|
1.25
|
DDME [15]
|
1.16
|
0.85
|
0.26
|
2.75
|
0.90
|
1.28
|
Yoo et al. [18]
|
1.15
|
0.37
|
0.26
|
4.53
|
0.90
|
1.27
|
Yoo et al. [17]
|
1.00
|
0.43
|
0.26
|
2.57
|
0.56
|
1.22
|
5. Conclusion
This paper reviewed the spatial and temporal color constancy methods, focusing on
temporal ones. The color constancy methods can be divided into statistics-, physics-,
and learning-based approaches. Several studies proposed using temporal features of
high-speed video, while most color constancy methods exploit spatial features of a
single image. The intensity of light sources supplied by alternative current varies
with time, which can be captured in high-speed video. The methods use this temporal
fluctuation as a prior of illuminant estimation. The periodic variation can be modeled
as a sinusoidal curve. This property is used to find AC pixels to estimate the accurate
dichromatic plane. In addition, it is used as temporal loss for training the network
that estimates dichromatic parameters. The intensity difference between frames can
be used to detect highly illuminated regions. The temporal correlation of high-speed
video was generated with a non-local neural network and contributes to illuminant
estimation. The experimental results confirmed that temporal features lead to better
color constancy.
ACKNOWLEDGMENTS
This work is supported by the National Research Foundation of Korea (NRF) grant
funded by the Korean government (MSIT) (No. 2020R1A4A4079705).
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Author
Jeong-Won Ha received her B.S. in electrical engineering from Korea University,
Seoul, Korea, in 2021. She is pursuing her M.S. in electrical engineering at Korea
University, Seoul, Korea. Her research interest includes color constancy, dichromatic
model, and intrinsic image decomposition.
Jong-Ok Kim received his B.S. and M.S. degrees in electronic engineering from Korea
University, Seoul, South Korea, in 1994 and 2000, respectively, and Ph.D. in information
networking from Osaka University, Osaka, Japan, in 2006. From 1995 to 1998, he served
as an Officer with the Korean Air Force. From 2000 to 2003, he was with the SK Telecom
Research and Development Center and Mcubeworks Inc., South Korea, where he was involved
in research and development on mobile multimedia systems. From 2006 to 2009, he was
a Researcher with the Advanced Telecommunication Research Institute International
(ATR), Kyoto, Japan. He joined Korea University, Seoul, in 2009, where he is currently
a Professor. His current research interests include image processing, computer vision,
and intelligent media systems. He was a recipient of the Japanese Government Scholarship,
from 2003 to 2006.