=Paper=
{{Paper
|id=Vol-1638/Paper30
|storemode=property
|title=Research of the atmospheric correction method based on approximate solution of modtran transmittance equation
|pdfUrl=https://ceur-ws.org/Vol-1638/Paper30.pdf
|volume=Vol-1638
|authors=Aleksander M. Belov,Vladislav V. Myasnikov
}}
==Research of the atmospheric correction method based on approximate solution of modtran transmittance equation ==
https://ceur-ws.org/Vol-1638/Paper30.pdf
Image Processing, Geoinformatics and Information Security
RESEARCH OF THE ATMOSPHERIC CORRECTION
METHOD BASED ON APPROXIMATE SOLUTION
OF MODTRAN TRANSMITTANCE EQUATION
A.M. Belov, V.V. Myasnikov
Samara National Research University, Samara, Russia
Abstract. The paper presents an experimental research of proposed method of
atmospheric correction of hyperspectral remote sensing data. The method is
based on approximate solution of MODTRAN transmittance equation using
simultaneous analysis of remote sensing hyperspectral image and an ideal hy-
perspectral image of the same territory. Results of experimental research imitat-
ing conditions of practical method usage are presented.
Keywords: hyperspectral image, remote sensing data, transmittance equation,
least square method, MODTRAN
Citation: Belov AM, Myasnikov VV. Research of the atmospheric correction
method based on approximate solution of modtran transmittance equation.
CEUR Workshop Proceedings, 2016; 1638: 256-262. DOI: 10.18287/1613-
0073-2016-1638-256-262
1 Introduction
Atmospheric correction is one of the important stages of remote sensing data pre-
processing especially in the case when the image analysis is based on the detected
radiance spectral components [1,2,3]. The difference between sensor detected radi-
ance and true surface radiance depends on many factors: solar declination, position of
satellite vehicle, imaging angle, composition and moisture of atmosphere, etc. All
these factors are taken into account in the generalized transmittance equation [4].
However, even with such detailed model of the atmosphere, it is difficult to solve
precisely the problem of atmospheric correction because of the large number of un-
known parameters which require a significant number of surface and meteorological
measurements. Furthermore, the observed surface is not Lambertian usually and it is
required to simulate a bidirectional reflectance distribution function for such surface
reflectance modeling, which also requires laboratory studies of the structural and
optical properties of materials [4].
There are a lot of methods and algorithms, that are used for the atmospheric correc-
tion of hyperspectral images: Scene-Based Empirical Approaches [5-8], Radiative
Transfer Modeling Approaches [9-11] and Нybrid Approaches [12-16]. The paper
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Image Processing, Geoinformatics and Information Security Belov AM. et al…
presents an experimental research of the method of atmospheric correction of remote
sensing hyperspectral images [15,16] which belongs to the hybrid approaches group.
The method is based on approximate estimation of parameters of simplified
MODTRAN transmittance equation. There is no need to model the atmosphere ex-
plicitly with this approach, the problem reduces to the determination of the unknown
coefficients of the equation, and all the details of light passing through the atmosphere
remain in the model. However, such a solution requires an ideal (i.e. free from atmos-
pheric distortions) hyperspectral image of the same territory. There is provided to use
low-flying airborne hyperspectral imaging or ground station hyperspectral imaging. It
is obvious that spatial resolution of the ideal image differs from the spatial resolution
of the distorted image, moreover a set of ideal images overlaps the distorted image
incompletely in common case. These facts require additional research.
2 Method overview
In the MODTRAN model the following simplification of transmittance is used [17]:
A(i, j ) B e (i, j )
L(i, j ) La (1)
1 e (i, j ) S 1 e (i, j ) S
where i 1 M , j 1 N are coordinates in image plane, L(i, j ) – detected radi-
ance, (i, j ) – target pixel reflectance, e (i, j ) – surrounding pixels reflectance, La
– radiance of the atmosphere backscattering, A, B – coefficients which depend on
atmospheric and geometry condition, S – atmospheric spherical albedo.
In common case values of A, B, S , La are calculated by the MODTRAN model [18],
however for the accurate calculation of these parameters it is necessary to have a
model of the atmosphere consistent to the place, time, and weather conditions of im-
aging. In the absence of necessary parameters of the atmosphere model it is possible
to perform atmospheric correction by an approximate solution of equation (1).
From each pixel of the ideal image we can define i, j and e i, j by averaging
within processing window. From atmospherically distorted image we can define
Li, j . Thus, it is necessary to determine the four unknown parameters: A, B, S , La .
The equation (1) is quadratic respective to the unknown parameters. However by
fixing a certain value La L*a we proceed to linear equation respective to the un-
known parameters A, B, S . Thus, writing equation (1) for each pair of corresponding
pixels of ideal and source HSI, we have an overdetermined system of MN linear
equations with three unknowns A, B, S .
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Image Processing, Geoinformatics and Information Security Belov AM. et al…
A1,1 B 1,1 S 1,1 L1,1 L* L1,1 L*
e e a a
A1,2 Be 1,2 Se 1,2 L1,2 L*a L1,2 L*a
. (2)
*
AM , N Be M , N Se M , N LM , N La LM , N La
*
To determine the unknown parameters it is proposed to use the method of least
squares.
A fixed value of the parameter La L*a is determined in accordance with assumption
that the value must be in interval 0, min La (i, j ) . Further, when iterating the interval
with the step L a , for each value L*a kLa , k is necessary to find a solution
x * A B S T of (2) and then choose the value of L*a kLa , k that mini-
mizes the error.
Atmospheric correction of distorted image is performed according to the formula
[17]:
Li, j La Li, j Le i, j
A
B (3)
A B Le i, j La S
where Le i, j - spatial averaging of the detected radiance, and the meaning of the
other parameters is similar to the equation (1).
The quality criterion of atmospheric correction based on a comparison of the ideal and
the corrected image which applied in experimental research is calculated as:
1 K
k
K k 1
where k - quality criterion for the certain spectral channel which is defined by the
following expression:
M N
I~k i, j Iˆk i, j
2
i 1 j 1
k
M N
I~k i, j 2
i 1 j 1
where I k i, j - sample of the ideal image, Iˆk i, j - sample of the corrected image.
~
In fact, the above mentioned criterion is the averaging of the standard deviation nor-
malized to the dynamic range of the channel of ideal image.
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3 Experimental results
We assume that ideal images and remote sensing data are obtained from different
sources and spatial resolution of ideal images is higher and a set of ideal images over-
laps a distorted image incompletely. Some experiments that imitate such conditions
were carried out. Hyperspectral image JasperRidge98av.img obtained from AVIRIS
aircraft was used as a source atmospherically-distorted image and the same image
corrected by FLAASH algorithm was used as an ideal image.
To research the efficiency of the algorithm in conditions when the spatial resolution
of source and ideal images differs following experiments were carried out:
A 256*256 pixels fragment of the ideal image was expanded by a factor of 2, 3 and 4.
An expansion was performed by pixel duplicating. In a similar way the ideal image
fragment was contracted by a factor of 2 and 4. Contraction was performed by pixel
averaging. Parameters of the transmittance equation were calculated using contracted
and expanded fragments. Atmospheric correction of the source image was performed
using calculated parameter sets. The quality criterion was calculated for corrected
images. Dependency of quality criterion from expansion and contraction factor E
presented on figure 1.
Presented graphics show that quality criterion varies slightly for an expansion case
and significantly for a contraction case. Thus we can conclude that proposed method
can satisfactory be used when spatial resolution of the ideal image is higher that spa-
tial resolution of source image and cannot be used in contrary.
2,00E-02
1,95E-02
1,90E-02
1,85E-02
1,80E-02
4,00 3,00 2,00 1,00
a)
1,01E+00
1,00E-02
1,00 0,75 0,50 0,25
b)
Fig. 1. Dependency of quality criterion from expansion and contraction factor E : a) expan-
sion, b) contraction
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Image Processing, Geoinformatics and Information Security Belov AM. et al…
To research an influence of percent of overlapping of source and ideal images S
following experiments were carried out:
Fragments of the ideal image that overlaps from 10 to 90 percent of source image in
horizontal and vertical way were obtained. Parameters of the transmittance equation
were calculated using these fragments. Atmospheric correction of the source image
was performed using calculated parameter sets. The quality criterion was calculated
for corrected images. Dependency of quality criterion from overlapping percent S
for a both cases presented on figure 2.
1,04E-01
5,40E-02
4,00E-03
100,00 70,00 40,00 10,00
a)
3,50E-02
2,50E-02
1,50E-02
5,00E-03
100,00 70,00 40,00 10,00
b)
Fig. 2. Dependency of quality criterion from overlapping percent S : a) vertical slicing, b)
horizontal slicing
Significant increasing of atmospheric correction quality for overlapping percent 20
and 30 gave us reason to carry out additional experiments. Dependency of quality
criterion for k from overlapping percent S was studied for certain spectral channels.
Experiment showed that such unexpected local quality increasing is typical for spec-
tral channels 144-224 (fig 3 b), for channels 1-143 dependency is monotonic increas-
ing (fig 3 a).
Further statistical analysis of the ideal image showed that channels 144-224 contain a
number of outliers affecting on parameters estimation and on atmospheric correction
quality respectively. This fact complains that we obtain a better quality while use a
reduced amount of source data. In this context there is a problem of increasing ro-
bustness of the method of atmospheric distortion parametric estimation. Since least
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Image Processing, Geoinformatics and Information Security Belov AM. et al…
squares method is high sensitive to outliers the idea for futher modification is to use a
special preprocessing algorithm in order to adjust data.
Conclusion
Experimental research showed that proposed method is applicable for practical usage
in atmospheric correction problem. Difference between reflectance values for ideal
and corrected images for some spectral channels showed that proposed method re-
quires a further modification aimed to adjust source data.
4,00E-04
3,50E-04
3,00E-04
2,50E-04
2,00E-04
90,00 70,00 50,00 30,00 10,00
a)
3,20E-01
2,20E-01
1,20E-01
2,00E-02
90,00 70,00 50,00 30,00 10,00
b)
Fig. 3. Dependency of quality criterion k from overlapping percent S for vertical slicing: a)
spectral channel 20, b) spectral channel 180
Acknowledgements
This work was financially supported by the Russian Scientific Foundation (RSF),
grant no. 14-31-00014 “Establishment of a Laboratory of Advanced Technology for
Earth Remote Sensing”
References
1. Denisova AYu, Myasnikov VV. Anomaly Detection for Hyperspectral Imaginery. Com-
puter Optics, 2014; 38(2): 287-296. [in Russian]
Information Technology and Nanotechnology (ITNT-2016) 261
Image Processing, Geoinformatics and Information Security Belov AM. et al…
2. Denisova AYu, Myasnikov VV. Algorithms of Linear Spectral Mixture Analysis for Hy-
perspectral Images Using Base Map. Computer Optics, 2014; 38(2): 297-303. [in Russian]
3. Kuznetsov AV, Myasnikov VV. A comparision of algorithms for supervised classification
using hyperspectral data. Computer Optics, 2014; 38(3): 494-502. [in Russian]
4. Schowengerdt R. Remote Sensing: Models and Methods for Image Processing (3rd Edi-
tion), Academic Press, 2006.
5. Chavez PS. An improved dark-object subtraction technique for atmospheric scattering cor-
rection of multispectral data. Remote Sensing of Environment, 1988; 24: 459-479.
6. Conel JE, Green RO, Vane G, Bruegge CJ, Alley RE. AIS-2 radiometry and a comparison
of methods for the recovery of ground reflectance. Proceedings of the 3rd Airborne Imag-
ing Spectrometer Data Analysis Workshop, 1987; 18-47.
7. Bernstein LS, Jin X, Gregor B, Adler-Golden S. Quick Atmospheric Correction Code: Al-
gorithm Description and Recent Upgrades. Optical Engineering, 2012; 51(11): 111719-1 –
111719-11.
8. Kruse FA. Use of airborne imaging spectrometer data to map minerals associated with hy-
drothermally altered rocks in the northern Grapevine Mountains, Nevada and California.
Remote Sens. Env., 1988; 24: 31-51.
9. Gao BC, Heidebrecht KB, Goetz AFH. Derivation of scaled surface reflectances from
AVIRIS data. Remote Sens. Env., 1993; 44: 165-178.
10. Gao BC, Davis CO. Development of a line-by-line-based atmosphere removal algorithm
for airborne and spaceborne imaging spectrometers. SPIE Proceedings, 1997; 3118: 132-
141.
11. Wu J, Wang D, Bauer ME. Image-based atmospheric correction of QuickBird imagery of
Minnesota cropland. Remote Sensing of Environment, 2005; 99: 315-325.
12. Goetz AFH, Heidebrecht KB, Kindel B, Boardman JW. Using ground spectral irradiance
for model correction of AVIRIS data. JPL Summaries of the 7th Annual Airborne Earth
Science Workshop, 1998; 98-1: 159-168.
13. Clark RN, Swayze GA, Heidebrecht KB, Green RO, Goetz AFH. Calibration to surface re-
flectance of terrestrial imaging spectrometry data: Comparison of methods. Summaries of
the 5th Annual JPL Airborne Earth Science Workshop, 1995; 95-1: 41-42.
14. Ardouin JP, Ross V. Methods for in-scene atmospheric compensation by endmember
matching. U.S. Patent No. 20,150,161,768. 11 Jun. 2015.
15. Belov AM, Myasnikov VV. Atmospheric correction of hyperspectral images using approx-
imate solution of MODTRAN transmittance equation. Computer Optics, 2014; 38(3): 489-
493. [in Russian]
16. Belov AM, Myasnikov VV. Atmospheric correction of hyperspectral images based on ap-
proximate solution of transmittance equation. Proc. SPIE 9445, Seventh International Con-
ference on Machine Vision (ICMV 2014), 2015; 94450S: S-1-5. DOI:10.1117/
12.2181364.
17. Yuanliu X, Runsheng W, Shengwei L, Suming Y, Bokun Y. Atmospheric correction of
hyperspectral data using MODTRAN model. SPIE Proceedings, 2003; 7123.
18. Kneizys FX, Robertson DC, Abreu LW, Acharya P, Anderson GP, Rothman LS,
Chetwynd JH, Selby JEA, Shettle EP, Gallery WO, Berk A, Clough SA, Bernstein LS.
The MODTRAN 2/3 Report and LOWTRAN 7 MODEL, Ontar Corporation, 1996.
Information Technology and Nanotechnology (ITNT-2016) 262