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

 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:

(x) = R

(x)T

(x) + A

(1 − T

(x)) (2)

(x) = e

−β

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

(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

(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 =

∑

[β

z(x) − log(T

(x))]

(4)

Taking the partial derivatives ∂ε/∂β

and ∂ε/∂z(x) of

the equation above and setting the derivatives to zero

results in the two equations:

∑

(x)z(x)

∑

(β

)

(5)

z(x) =

∑

(x)β

∑

(β

)

(6)

Using the above equations we are able to repeatedly

iterate between solving for β

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

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

VISAPP 2010 - International Conference on Computer Vision Theory and Applications

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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