MEASURING ATMOSPHERIC SCATTERING FROM DIGITAL
IMAGE SEQUENCES
Tarek El-Gaaly and Joshua Gluckman
Computer Science Department, The American University in Cairo, Egypt
Keywords:
Atmospheric scattering, Haze, Image, Dehazing, Depthmap.
Abstract:
Current environmental monitoring devices are limited in their capability of measuring atmospheric particulate
matter (PM) over large areas. Quantifying the visual degrading effects of atmospheric scattering in digital
images of urban scenery and correlating these effects to PM levels is a vital step in more practically moni-
toring our environment. Currently, image haze removal (or dehazing) techniques exist which remove all the
haze from a scene for the sole purpose of enhancing vision. This paper presents an extension to existing de-
hazing algorithms to use sequences of images captured over time and enforce a constant depth constraint. An
experimental comparison of dehazing algorithms is then presented in the context of measuring atmospheric
scattering and depth recovery using both simulation and depth measurements from real data.
1 INTRODUCTION
How air pollution affects the visual appearance of
scenes has been a research challenge for scientists.
Changes in emissions, urban growth, and many other
factors influence the amount and type of air pollution.
Suspended particulate matter (PM) in the atmosphere
visually degrades urban scenery. Understanding the
visual effects of the atmosphere over large urban ar-
eas captured in ground-based digital images is a vital
step in measuring global levels of PM over large areas
more practically.
Atmospheric scattering fluctuates proportionally
to the level of PM in the atmosphere (Vollmer, 2003;
Jacobson, 2005; Kokhanovsky, 2003) and therefore
offers a way of measuring PM through visual means.
The challenge of measuring atmospheric scattering
visually lies in finding the relationship between im-
age pixel intensities and atmospheric scattering taking
place in the scene. The difficulty of finding this rela-
tionship lies in accounting for the many factors that
affect the pixel values, such as: physical scattering of
light by molecules and suspended particles, position
of the sun, geometric and radiometric camera calibra-
tion, multiple-scattering, ground and object reflection,
the presence of non-spherical particles and variations
in background scene radiance due to changes in illu-
mination (Kokhanovsky, 2003; Jacobson, 2005).
Currently, haze removal (or dehazing) algorithms
exist which remove most of the haze in a scene. This
is ideal from the perspective of enhancing vision but
finding the relationship between the extracted haze
and global PM levels from ground-based images is an
under researched problem.
In the context of measuring atmospheric scattering
visually, three existing dehazing algorithms are ana-
lyzed and compared. The first is a polarization-based
dehazing method (Schechner et al., 2003; Shwartz
et al., 2006). Two or more images are captured
with different degrees of polarization (using a po-
larizer filter). The second is the dichromatic frame-
work (Narasimhan and Nayar, 2000) which dehazes
using multiple images of the same scene under dif-
ferent weather conditions. The third dehazing algo-
rithm is a more recent approach which uses a statisti-
cal prior called the ’Dark Channel’ to dehaze a single
image (He et al., 2009). This prior is based on ob-
served statistics of outdoor images free of haze. It
is based on the observation that the majority of lo-
cal patches in outdoor haze-free images contain pixels
which have very low intensities in at least one color
channel. Other more recent methods which emerged
through the course of this research are: single image
dehazing (Fattal, 2008) and visibility in bad weather
from a single image (Tan, 2008). The latter uses
the observation that haze-free images naturally have
higher contrast and hence dehazing is done by max-
imizing the local contrast. Fattal assumes that atmo-
spheric transmission and surface shading are locally
uncorrelated.
376
El-Gaaly T. and Gluckman J. (2010).
MEASURING ATMOSPHERIC SCATTERING FROM DIGITAL IMAGE SEQUENCES.
In Proceedings of the International Conference on Computer Vision Theory and Applications, pages 376-381
DOI: 10.5220/0002829103760381
Copyright
c
SciTePress
Some methods exist which require additional in-
formation, such as (Kopf et al., 2008; Narasimhan and
Nayar, 2003). These methods require additional depth
knowledge of the scene.
The first contribution of this research is the exten-
sion of existing dehazing algorithms to use sequences
of images captured over time. An optimization al-
gorithm enforces a constant depth constraint over the
sequence of images and allows the decomposition of
the scene into a sequence of atmospheric scattering
coefficients and a relative depthmap. The second con-
tribution is an experimental comparison of dehazing
algorithms, in the context of measuring atmospheric
scattering and depth recovery, using both simulation
and depth measurements from real data.
2 BACKGROUND
In computer vision and graphics, the widely used
model for describing the formation of haze in images
is as follows (Tan, 2008; Fattal, 2008; Narasimhan
and Nayar, 2000; Narasimhan and Nayar, 2002):
I = Re
βz
+ A
(1 e
βz
) (1)
where I is the observed image intensity, R is the
scene radiance, A
is the global atmospheric airlight,
β is the atmospheric scattering coefficient and z is
the depth of the scene. The term e
βz
represents the
medium transmission describing the fraction of light
that is not scattered as it passes through the medium.
This model assumes a homogeneous atmosphere.
The term Re
βz
of equation 1 is known as the di-
rect transmission, and the second term A
(1 e
βz
)
is known as airlight. Direct transmission is the part of
scene radiance that eventually reaches the viewpoint
after suffering attenuation as it passes through the
medium. Airlight results from light scattered by the
medium towards the viewpoint and causes an increase
in brightness as the depth of the scene increases.
This research focuses on three existing dehazing
methods. Each of them dehaze an image of a scene
and produce a relative depthmap scaled to the atmo-
spheric scattering coefficient β (in equation 1). The
polarization-based dehazing method uses a sequence
of two or more images captured with different degrees
of polarization. The degree of polarization is varied
by varying the angle of a polarizer filter attached to a
camera. Using the difference in intensity of airlight
between the images and the haze image model (equa-
tion 1) the scene is dehazed and a depthmap is pro-
duced. The ’Dichromatic Framework’ measures at-
mospheric scattering using changes in weather condi-
tions. The color of a scene point is modeled as a linear
combination of direct transmission and airlight vec-
tors in a color space. The color of a scene point may
vary anywhere within the plane (dichromatic plane)
defined by the vectors. The ’Dark Channel’ method
uses a statistical prior to dehaze a haze-filled input
image. It uses the observation that outdoor haze-filled
images are composed of local patches which contain
pixels with very low intensity in at least one color
channel. This is due to the overwhelming presence
of shadows, colorful surfaces and dark surfaces.
3 CONSTANT DEPTH
CONSTRAINT
The Constant Depth Constraint (CDC) is based on the
fact that the scene being captured in the form of im-
ages over time has constant depth. This algorithm
is based on the haze image model (equation 1). The
model is rewritten as follows:
I
c
i
(x) = R
c
(x)T
i
(x) + A
c
(1 T
i
(x)) (2)
T
i
(x) = e
β
i
z(x)
(3)
The superscript signifies that the coefficient is defined
over the three color channels (RGB). The subscript
signifies that the variable varies over time. T
i
(x) is
the global transmittance of each image captured at
time i. x is the spatial index corresponding to square
patches over the images. The scene radiance R
c
(x)
varies as the illumination due to the sun in the scene
changes direction. This variation is assumed to be
small over the limited period of time the sequence of
images are captured over (see Figure 2). In addition to
this assumption, we performed a normalization tech-
nique on the sequence of images captured of the same
scene. We choose a flat surface in the scene and nor-
malized our radiance measurements by the radiance
of this surface. As the illumination changes in the
scene, the radiance of this flat surface varies with it
and by using this to normalize the scene radiance of
each image we essentially factor out the variation be-
tween the sequence of images. The flat surface chosen
in the scene can be seen in Figure 1.
The CDC constraint is used to form an opti-
mization algorithm to recover a sequence of atmo-
spheric scattering coefficients corresponding to the
sequence of images captured over time and one sin-
gle depthmap of the scene. The algorithm is based on
the relation between the transmittance, atmospheric
scattering and depth in equation 3 under the con-
straint of constant depth of the scene (CDC). This
MEASURING ATMOSPHERIC SCATTERING FROM DIGITAL IMAGE SEQUENCES
377
Figure 1: The flat surface of the scene used to normalize the
radiance of each image and therefore account for the change
in illumination. It can be seen in the lower left hand side of
the scene.
optimization algorithm extends the existing dehazing
techniques. The CDC improves the accuracy of the
relative depthmap recovered by each dehazing tech-
nique by factoring the scaled depthmap into a set of
atmospheric scattering coefficients (one for each im-
age) and one single depthmap, no longer scaled by the
atmospheric scattering coefficient.
A solution is found by implementing a standard
least squares regression to find the best fit variables
in the transmittance model (equation 3). Accordingly,
equation 3 yields the following error function to min-
imize:
ε =
i
x
[β
i
z(x) log(T
i
(x))]
2
(4)
Taking the partial derivatives ∂ε/∂β
i
and ∂ε/z(x) of
the equation above and setting the derivatives to zero
results in the two equations:
β
i
=
x
T
i
(x)z(x)
x
(β
i
)
2
(5)
z(x) =
i
T
i
(x)β
i
i
(β
i
)
2
(6)
Using the above equations we are able to repeatedly
iterate between solving for β
i
and then solving for
z(x) until they converge.
The algorithm for this optimization is as follows:
For each patch
while delta of Beta is not close to 0
Beta <- min(Beta,1)
Beta <- max(Beta,0)
z <- max(z,0)
Compute Beta using equation 5
Clamp Beta of image with
maximum atmospheric airlight to 1
Compute z using equation 6
end
end
As there may be multiple possible solutions in the
solution space, the maximum atmospheric scattering
coefficient of the sequence of images is clamped to
1 and all other scattering coefficients are scaled with
respect to it. The maximum scattering coefficient is
chosen as the brightest image (i.e. the image with
the maximum atmospheric airlight intensity measured
from the low sky region). In addition to this the depth
is clamped above 0 to avoid negative depth estimates.
The scattering coefficients are also clamped to values
between 0 and 1.
The algorithm described above converges to an
unscaled relative depthmap and a set of scattering co-
efficients (one per image). This optimization extends
existing dehazing algorithms and allows the accuracy
of the measured scattering coefficients and the recov-
ered depthmap to be compared. This algorithm con-
verges to a depthmap no longer scaled by the atmo-
spheric scattering coefficient and therefore is more
accurate. There are two benefits of this optimization
model. From the perspective of atmospheric scatter-
ing, an estimate of the atmospheric scattering coeffi-
cients for each captured image is derived by apply-
ing our model to a sequence of images of the same
scene, as seen in Figure 2. From the point of view of
the accuracy of the recovered relative depthmap the
accuracy is increased by factoring out the scattering
coefficient scaling factor.
4 EXPERIMENTAL RESULTS
The existing dehazing algorithms were compared in
the context of atmospheric scattering measurement by
extending each algorithm with the CDC optimization
and applying them to simulated haze images. We used
the model of haze described in equation 1 to synthe-
size simulated haze scenes. We injected errors into
different parameters of the dehazing algorithms to see
the effects on the accuracy of the measured atmo-
spheric scattering coefficient.
Our first observation is that the polarization-based
dehazing algorithm suffers with a small error in the
degree of polarization (Figure 3). The polarization-
based dehazing is naturally dependent on the degree
of polarization. When a small error is injected into
it, this technique is the most accurate in measuring
the atmospheric scattering. When the error in polar-
ization increases slightly, as can be seen in Figure
3, we see a large decrease in the accuracy of the at-
mospheric scattering. The polarization parameter in
the polarization-based dehazing algorithm is a scalar
VISAPP 2010 - International Conference on Computer Vision Theory and Applications
378
Figure 2: A sequence of four images of the same scene taken at constant intervals over time. A slight variation in the
illumination of the scene is evident.
Figure 3: The accuracy of the measured atmospheric scattering of the haze simulations for the three dehazing algorithms as
an error in degree of polarization is increased: polarization dehazing with CDC (POL-CDC), dichromatic dehazing with CDC
(DICH-CDC) and dark channel dehazing with CDC (DC-CDC). Fluctuations in the methods is due to random generation of
the simulated scene radiance.
Figure 4: The figure shows the dehazing methods compared to each other. Clearly the dichromatic framework displays the
worst performance. The polarization dehazing shows the least error as image noise increases. The dark channel decreases at
first with low noise but then rises with high noise. No error is injected into the degree of polarization (perror = 0).
value from 0 to 1. The dichromatic framework per-
forms well under no noise but as soon as a small
amount of noise is introduced it becomes the least
accurate approach falling below the other two algo-
rithms (Figure 4). The dark channel starts off with a
larger error than the other two dehazing methods. It
initially improves under low noise but then worsens as
noise increases (Figure 4). This unstable trend in the
accuracy of the dark channel may be due to the fact
that this technique is highly dependent on color in-
formation in the images. In some situations the dark
channel of a part of the image is not small and neg-
ligable. This happens due to surfaces in the image
with similar radiance to that of the haze in the scene
MEASURING ATMOSPHERIC SCATTERING FROM DIGITAL IMAGE SEQUENCES
379
Figure 5: The figure shows the polarization dehazing with CDC (POL-CDC). As the image noise increases the error increases
in general. There are four different plots for the POL-CDC with different values of the degree of polarization p.
Figure 6: The two reference regions of the scene used to
compute the distance ratio from Google Maps. The dis-
tance to the billboard in the scene above is approximately
2.2 km. The distance to the flat surface of the building in
the foreground is approximately 493.9 m.
(He et al., 2009). This distorts the accuracy of the
measured atmospheric scattering. Therefore increas-
ing image noise greatly affects the color information
in the images and hence greatly affects the accuracy
of the dark channel method. The polarization dehaz-
ing outperforms the other dehazing algorithms as im-
age noise increases and as the degree of polarization
varies within realistic bounds we see no significant
change in the accuracy of this approach (Figure 5).
In order to verify the accuracy of the unscaled
depthmaps recovered by each of the existing dehaz-
ing algorithm with and without the CDC extension,
we gathered ground truth measurements from Google
Maps. We measured the distances between the view-
point and the two relatively flat regions shown in Fig-
ure 6 by locating them on Google Maps. The ratio
of these two distances is what we use to compare the
relative depthmaps.
As you can see from Table 1, the CDC optimiza-
tion algorithm increases the accuracy of the recovered
depthmap by factoring out the atmospheric scatter-
ing scalar. This is done by optimizing according to
the constraint of constant depth of a scene over time
(CDC). For this reason all the dehazing algorithms an-
alyzed are improved when the CDC is applied to its
output. The CDC optimization enhances the accuracy
of the polarization dehazing algorithm by approxi-
mately 4% and enhances the accuracy of the dark
channel by approximately 42%. It should be noted
that our implementation of the dark channel method
does not include the soft matting which does improve
the dehazing of this method. This requires further
investigation to determine how much more accurate
in measuring atmospheric scattering the dark chan-
nel method becomes with soft matting applied. Dif-
ferences between the accuracy of the methods could
be due to different unknown scale factors in each de-
hazing method. For example, the polarization method
may introduce linear or non-linear scale factors in the
process of filtering the light through the polarizer fil-
ter. There are many other unknown scale factors such
as: ground-reflection, ambient light, variation in il-
lumination and occlusions. The many possible scale
factors are too many to fully account for in the scope
of this research.
Table 1: The distance ratio returned by each algorithm av-
eraged across the regions of the image shown in Figure 6.
Algorithm Distance Ratio
Ground truth (using Google Maps) 4.50
POL 3.55
POL-CDC 3.69
DC 0.59
DC-CDC 0.83
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380
5 CONCLUSIONS
We have presented two contributions in this research.
The first is an investigation into dehazing meth-
ods to be used for measuring atmospheric scattering
from images. We extend each dehazing method to
use a sequence of images captured over time. The
polarization-based dehazing has initially shown it is
the most accurate method provided the degree of po-
larization is large enough to be detected between the
images and there is no significant error in the degree
of polarization. The second contribution is the CDC
optimization which extends each dehazing algorithms
to recovering a more accurate unscaled depthmap of
the scene.
There is still much more room for research in this
area. One future work can be to correlate the at-
mospheric scattering to PM levels measured by con-
ventional devices (Eiseman, 1998a; Eiseman, 1998b).
More dehazing methods should be investigated and
compared to the three dehazing algorithms we have
analyzed in this research. More research can be done
in separating the two parts of haze (natural molecular
and PM parts) to more accurately determine the level
of PM from images. Other visual data can be ana-
lyzed to measure atmospheric scattering such as video
streams. The methods of measuring depth and atmo-
spheric scattering recovered can be applied to further
dehaze the scene more accurately.
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