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Relation between degree of polarization and Pauli color coded
image to
characterize scattering mechanisms
Sanjit Maitra*a, Michael G. Gartleya and John P. Kerekesa
aDigital Imaging and Remote Sensing Laboratory, Chester F. Carlson
Center for Imaging Science,
Rochester Institute of Technology, 54 Lomb Memorial Drive,
Rochester, NY 14623,USA
ABSTRACT
Polarimetric image classification is sensitive to object
orientation and scattering properties. This paper is a preliminary
step to bridge the gap between visible wavelength polarimetric
imaging and polarimetric SAR (POLSAR) imaging scattering
mechanisms. In visible wavelength polarimetric imaging, the degree
of linear polarization (DOLP) is widely used to represent the
polarized component of the wave scattered from the objects in the
scene. For Polarimetric SAR image representation, the Pauli color
coding is used, which is based on linear combinations of scattering
matrix elements. This paper presents a relation between DOLP and
the Pauli decomposition components from the color coded Pauli
reconstructed image based on laboratory measurements and first
principle physics based image simulations. The objects in the scene
are selected in such a way that it captures the three major
scattering mechanisms such as the single or odd bounce, double or
even bounce and volume scattering. The comparison is done between
visible passive polarimetric imaging, active visible polarimetric
imaging and active radio frequency POLSAR. The DOLP images are
compared with the Pauli Color coded image with |HH-VV|, |HV|, |HH
+VV| as the RGB channels. From the images, it is seen that the
regions with high DOLP values showed high values of the HH
component. This means the Pauli color coded image showed
comparatively higher value of HH component for higher DOLP compared
to other polarimetric components implying double bounce reflection.
The comparison of the scattering mechanisms will help to create a
synergy between POLSAR and visible wavelength polarimetric imaging
and the idea can be further extended for image fusion.
Keywords: Degree of Linear Polarization (DOLP), Polarimetric SAR
(POLSAR), Pauli Color coded image, passive polarimetry
1. INTRODUCTION Polarimetric SAR data has its application in
flood mapping, estimation of biophysical characteristics such as
biomass, basal area, soil moisture, snow density, land cover
classification and many more1-5. In polarimetric SAR, the emitted
and the received states of polarization are changed during data
collection6. For a particular scene, a fully polarimetric SAR data
comprises of four channels for the four different combinations of
transmitted and received radar wave (HH, HV, VH and VV). It
provides the phase and magnitude of the backscattered radar signal
that is related to the material properties, orientation, roughness,
etc of the target in the scene. In EO/IR polarimetric imaging, the
received polarization states are changed to measure the Stokes
parameters7. Degree of linear polarization (DOLP), widely used in
the EO/IR community, is derived from the Stokes parameters to study
target behavior in the scene.
This paper attempts to find a relationship between polarimetric
SAR data represented in Pauli color code to Degree of Linear
Polarization (DOLP) in the visible passive polarimetric imaging. An
intermediate active visible polarimetric imaging mode is also
considered where the images are recorded with polarizer both in
front of the source and the detector to generate the Pauli color
coded image in the visible domain. This mode will have its
application in active polarimetric imaging such as polarimetric
LIDAR. The active and passive visible polarimetric imaging is done
through laboratory measurements and the same scene is simulated in
DIRSIG (Digital Image and Remote Sensing Image Generation) which is
developed by Rochester Institute of Technology’s Digital Imaging
and Remote Sensing Laboratory for the polarimetric SAR data. DIRSIG
uses Stokes Vector and Mueller Matrix calculations to simulate the
scene8.
*[email protected]; www.cis.rit.edu
Polarization: Measurement, Analysis, and Remote Sensing Xedited
by David B. Chenault, Dennis H. Goldstein, Proc. of SPIE Vol. 8364,
83640F
© 2012 SPIE · CCC code: 0277-786X/12/$18 · doi:
10.1117/12.918486
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2. THEORY The three major scattering mechanisms that are widely
used in the radar community are single bounce from a plane surface
backscattered towards the radar (Figure 1(a)), double bounce from
one flat surface that is horizontal with an adjacent vertical
surface (Figure 1(b)) and volume scattering from randomly oriented
scatterers (Figure 1(c)). We can consider these three scattering
mechanisms as three classes that get separated in a polarimetric
SAR image. Pauli color coded representation can be used to visually
differentiate the three major scattering mechanisms. A Pauli color
coded image is based on linear combinations of the polarimetric SAR
channels (HH, HV, VH and VV). The polarimetric channels |HH-VV|,
|HV| and |HH+VV| are assigned to the RGB channels respectively9.
Figure 2 shows a comparison between RGB image of an area south of
San Francisco, CA (Courtesy Google Earth, USDA Farm Service Agency,
GeoEye and US Geological Survey) and a polarimetric SAR image of
the same area (Courtesy NASA/JPL-Caltech) displayed in the Pauli
Color coded representation. The POLSAR image shown in the Pauli
color format appears as a class map with the three major scattering
mechanisms as the classes. Single Bounce scattering from the lake
in the scene appears bluish black which indicates large values of
|HH+VV| component compared to other polarimetric channels. The
buildings in the scene appear purple implies comparative large
values for red and blue channels i.e. comparative high |HH-VV|
value denoting double bounce scattering. The vegetation in the
scene appears green in color which means high |HV| for volume
scattering. So in the Pauli Color image, the bluish black is for
the single first surface bounce, red/purple is for double bounce
and green for the multiple scattering.
(a) (b) (c)
Figure 1. Three major scattering mechanisms (a) single bounce
(b) double bounce (c) multiple bounces
(a) (b)
Figure 2. (a) Google Earth RGB image of a region south of San
Francisco. Courtesy Google Earth, USDA Farm Service Agency, GeoEye
and US Geological Survey (b) NASA UAVSAR L-band Polarimetric SAR
image of the same area with |HH-VV|, |HV| and |HH+VV| as the RGB
channels. Courtesy NASA/JPL-Caltech
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3. MATHEMATICAL RELATION The four Stokes vector10 elements in
terms of the intensity images are given as
S0 = I0 + I90 (1)
S1 = I0 – I90 (2)
S2 = I45 – I135 (3)
S3 = IRCP – ILCP (4)
where I0, I90, I45, I135, IRCP, ILCP are intensity images
through polarizer orientated at 0°, 90° ,45°, 135° and through
right and left circular polarizer respectively.
The degree of linear polarization in terms of Stokes vector
elements is given as
DOLP = √{ S1 2 + S2 2 } / S0 (5) From eqn.5 we can say that DOLP
is proportional to the difference between horizontal and vertical
polarization normalized by the total intensity of light. In case of
polarimetric SAR, IHV is considered here as the image corresponding
to horizontal polarization transmit and vertical polarization
receive radar. So for a fully polarimetric SAR collection, the four
channels are IHH , IHV , IVH and IVV. So, the total horizontal
polarized signal received is
I0Radar = IHH + IVH (6) and the total vertical polarized signal
received is
I90 Radar = IVV + IHV (7) Comparing eqn.6 and 7 with eqn.5,
DOLPRadar ∝ {(IHH + IVH) – (IVV + IHV)} / (IHH + IVH + IVV +
IHV) (8)
Usually IVH and IHV are generally highly correlated in
polarimetric SAR. So, eqn.8 can also be written as,
DOLP ∝ (IHH - IVV) / (IHH + IVV + IVH + IHV) (9)
Eqn.9 mathematically shows that DOLP is proportional to the
ratio of the Pauli red channel (IHH - IVV) and the Pauli blue
channel (IHH + IVV).
4. EXPERIMENTAL SETUP The three major scattering mechanisms are
investigated in passive polarimetric, active polarimetric and
polarimetric SAR mode. The passive visible polarimetric imaging
mode (shown in fig. 3(a)) is the conventional polarimetric imaging
mode that is used widely in remote sensing applications. In this
case, we have a polarizer in front of the sensor and for four
different orientations of the polarizer (0°, 45°, 90° and 135°) we
record the I0 , I45 , I90 and I135 images. Using equations 1-4, the
Stokes vector elements are calculated and DOLP is computed for each
scene using eqn.5. The active visible polarimetric imaging mode
(shown in fig. 3(b)) is an unique data collection mode where we
have polarizer both in front of the source and the sensor. The
polarizer in front of the source is oriented with its pass axis
horizontal and the polarizer in front of the sensor is oriented to
receive vertical polarized wave to capture the IHV image. Similarly
both the polarizers are rotated to record IHH, IVH and IVV images.
Pauli color coded image are produced using |HH-VV|, |HV|, |HH +VV|
as the RGB channels. This mode of data collection is similar to the
polarimetric SAR mode. For both the modes, the same sensor and
source were used for the same scene during data collection. The
measurements in the laboratory for the visible polarimetric imaging
are done using a fiber optic quartz halogen light source with a
spectral range of 400-1500nm. A 782 x 582 pixel camera is used to
record the panchromatic images with spectral sensitivity range of
400-1000nm. Wire grid polarizers with moderate extinction ratio
were used.
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The SAR modeling capability of DIRSIG has been improved since
last reported8 to include a four channel (HH, HV, VH and VV)
polarization sensitive antenna. In contrast to unpolarized SAR
simulations, the four channel simulations utilize complex valued
Stokes vectors and Mueller Matrices for radiative transfer
calculations. Currently, the simulations assume simultaneous
transmit of horizontal and vertical polarization from the same
phase center. Additionally, the model utilizes a simple micro-facet
radar cross section (RCS) density model to define each material
surface. The user is able to vary the complex permittivity,
root-mean-square surface slope, and level of diffuse scattering
under the assumptions of Geometric Optics. Furthermore, the user
has the ability to specify the number of subsequent photon bounces
between scene surfaces before ending the ray tracing process,
enabling a variety of multi-bounce phenomenologies to be studied in
detail. Future model updates will include integration of a fully
polarimetric Physical Optics based scattering model valid over a
wider range of conditions. The radar parameters used in the
simulation is given in table 1.
(a) (b) (c) Figure 3. Different Imaging modes investigated (a)
Passive visible polarimetric (b) Active visible polarimetric and
(c) Polarimetric SAR. Table 1. Radar Parameters used in the DIRSIG
simulations.
Parameter Value Wavelength 31.2 cm Pulse Duration 15 μs
Polarization Quad(HH, HV, VH, VV) Altitude 15,000 m Ground Speed
200 ms-1
Range direction look angle 45° Pulse period 10ms
5. RESULTS Fig. 4(a) is the intensity image of miniaturized car
models with the fiber optic light source and the corresponding DOLP
image is shown in 4(b). The S0 image of real cars with sun as the
source is shown in 4(c). This comparison shows that the
investigations done in the laboratory can be extended to passive
polarimetric images with sun as the source. The major difference
between the two is the effect of the polarization pattern of the
sky which can clearly be seen on the windshield of the car in fig.
4(d). This effect is not present in the DOLP image recorded in the
lab.
(a) (b) (c) (d) Figure 4. Comparison of images taken in the
laboratory with fiber optic light source and image of a parking lot
with real cars and sun as the source (a) S0 intensity image in the
laboratory with miniaturized model of cars (b) Corresponding DOLP
(c) S0 intensity image of a parking lot with sun as the source (d)
Corresponding DOLP image.
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5.1 Single bounce
A plane object with aluminum foil wrapped around is used to
demonstrate the single bounce scattering mechanism. The total
intensity S0 image is shown in fig. 5(a). The DOLP image (fig.
5(b)) showed lower values at the pixel locations with higher S0
values. The image shown in fig. 5(b) has minimum DOLP value of 0
and a maximum value of 0.7861. The Pauli color image (fig. 5(c))
showed higher |HH + VV| values. The simulated synthetic object is
shown in figure 5(d). The radar is located at a position that is
normal to the surface, to capture the single bounce from the
surface. The Pauli color image from the DIRSIG output also appears
blue for the single surface scattering (fig. 5(e)). In this case
the |HH-VV| and |HV| channel are zero. All the POLSAR images shown
in this paper are rotated 90° for the comparison with visible
polarimetric images such that the x-axis of the images is the
azimuth and the y-axis is the range direction of the radar.
(a) (b) (c)
(d) (e) Figure 5. Demonstrating single Bounce scattering in the
three different modes (a) Total intensity S0 image (b) DOLP (c)
Pauli Color coded image (d) Blender screenshot of the object used
in the DIRSIG simulation (e) Pauli Color coded image from the
simulation output. 5.2 Double bounce
A dihedral object was used to investigate the double bounce
phenomenon in different imaging modes. The DOLP image (fig. 6(b))
has minimum value of 0 and maximum value of 0.754. The Pauli image
(fig. 6(c)) shows purple appearance which is a combination of blue
and red. The object in the simulated image is orientated such that
the radar is at angle of 45 degree from the normal of the
horizontal surface of the dihedral. The red channel (|HH-VV|) and
the blue channel (|HH+VV|) are shown in fig. 6(e) and fig. 6(f)
respectively. The Pauli image generated from the DIRSIG output
(fig. 6(g)) appears purple. The DOLP value is comparatively high
for the double bounce effect and also the |HH-VV| is high in this
case both in the visible and the POLSAR Pauli image. The |HV|
channel is zero for all the modes.
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(a) (b) (c)
(d) (e) (f)
(g) Figure 6. Demonstrating double bounce scattering in the
three different modes (a) Total intensity S0 image (b) DOLP (c)
Pauli Color coded image (d) Blender screenshot of the object used
in the DIRSIG simulation (e) |HH-VV| channel from the DIRSIG output
(f) |HH+VV| channel from the DIRSIG output (g) Pauli Color coded
image from the simulation output. 5.3 Multiple bounce
Clump-foliage is used as the object to demonstrate multiple
scattering which is widely used to model shrubs and bushes. The
DOLP image (fig. 7(a)) has a maximum value of 0.6276 and a minimum
value of zero. The higher DOLP value at the left side is due to the
shadow of a portion of the foliage. The green and blue channel in
this case is nearly zero so the Pauli image (fig. 7(c)) is greenish
signifying higher |HV| component. A green tinge throughout the
image is due to the leakage of the polarizers used. In case of the
DIRSIG simulation, we get the |HH+VV| and the |HV| component. The
red |HH-VV| channel is zero. The blue component is for the first
surface bounce from the object and the green component is for the
multiple scattering.
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(a) (b) (c)
(d) (e) (f)
(g) Figure 7. Demonstrating multiple bounce scattering in the
three different modes (a) Total intensity S0 image (b) DOLP (c)
Pauli Color coded image (d) Blender screenshot of the object used
in the DIRSIG simulation (e) |HV| channel (f) |HH+VV| channel (g)
Pauli Color coded image from the simulation output. 5.4 Complex
real life object A miniaturized car model is also used to
investigate a real world object. The DOLP (fig. 8(b)) image showed
higher values in the reflection from the front bumper of the car.
The maximum value of DOLP is 0.6912. The Pauli image in fig. 8(c)
shows a purple tinge in the same area corresponding to higher DOLP
value. This signifies both single and double bounce from the front
bumper of the car. A greenish appearance throughout the Pauli image
is again because of the leakage of the polarizers used. In this
demonstration the ground surface is critical as the double bounce
is between the front bumper and the ground. So, in the DISIRG
simulation, a ground surface is included with about 20%
specular
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reflection. The car model used is similar to the miniaturized
car used for the DOLP image (fig. 8(b)). In the DIRSIG output we
see that that double bounce is prominent from the front bumper of
the car from the |HH-VV| image. A contrast enhancement is done for
the red channel |HH-VV| image (fig. 8(e)) to display the double
bounce effect from the dihedral formed by the bumper of the car and
the ground.
(a) (b) (c)
(d) (e) (f) Figure 8. Demonstrating scattering from a complex
object in the three different modes (a) Total intensity S0 image
(b) DOLP (c) Pauli Color coded image (d) Blender screenshot of the
object used in the DIRSIG simulation (e) |HH-VV| channel (Contrast
enhanced) (f) Pauli Color coded image from the simulation
output
6. CONCLUSIONS AND FUTURE WORK DOLP image using passive
polarimetric imaging and the Pauli Color image for visible and
radio waves are compared for the three basic scattering mechanisms.
In case of single bounce, we observe low values of DOLP and high
values of |HH+VV| both in the laboratory results and DIRSIG output.
Results showed comparatively higher values of DOLP for double
bounce and corresponding Pauli color images showed higher values of
|HH-VV| component. For multiple bounce, lower DOLP values were seen
with high values of |HV|. The relationship of DOLP with Pauli color
image is discussed mathematically also. It is seen that higher DOLP
value corresponds to high HH component which increase the |HH-VV|
component in the Pauli color coded image. The major challenge was
to match the material properties of the actual objects and the
simulated objects at the radar wavelength. Estimation of the
object’s material properties at the radar wavelength is critical. A
rigorous quantitative relation needs to be established between DOLP
and Pauli color components. Once a relationship between widely used
modalities of polarimetric imaging are determined, enhanced
information extraction will be possible using image fusion, and
further extended across different modes of polarimetric
imaging.
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7. ACKNOWLEDGEMENTS RIT would like to thank Lockheed Martin
Information Systems and Global Services for partial funding of this
work. The authors would like to thank NASA Jet Propulsion
laboratory, California Institute of Technology for providing the
fully polarimetric UAVSAR data.
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