Relation between degree of polarization and Pau li color ... · Relation between degree of...

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

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Proc. of SPIE Vol. 8364 83640F-1

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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



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.



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.



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.



(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.



(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



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.



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.

REFERENCES

[1] Hess, L.L., Melack, J.M., Filoso, S. and Wang, Y., “Delineation of Inundated Area and Vegetation Along the Amazon Floodplain with the SIR-C Synthetic Aperture Radar,” IEEE Transaction on Geoscience and Remote Sensing, Vol.33,No. 4, 896-904 (1995).

[2] Dobson, M.C., Ulaby, F.T., Pierce, L.E., Sharik, T.L., Bergen, K.M., Kellndorfer, J., Kendra, J.R., Li, E., Lin, Y.C., Nashashibi, A., Sarabandi, K. and Siqueira, P., “Estimation of Forest Biophysical Characteristics in Northern Michigan with SIR-C/X-SAR,” IEEE Transaction on Geoscience and Remote Sensing, Vol. 33, No. 4, 877-895 (1995).

[3] Hajnsek, I., Pappathanassiou, K.P., Reigber, A., Cloude, S.R., “Soil-moisture estimation using polarimetric SAR data,” Geoscience and Remote Sensing Symposium, IGARSS '99 Proceedings, IEEE 1999 International, vol.5, 2440-2442 (1999).

[4] Li, Z., Guo, H., Shi, J., “Estimation of snow density with L-band polarimetric SAR data,” Geoscience and Remote Sensing Symposium, IGARSS 2000 Proceedings, IEEE 2000 International, vol.4, 1757-1759 (2000).

[5] Rodrigues, A., Corr, D.G., Pottier, E. and Hoekman, D., “Land Cover Classification using Polarimetric SAR data,” Interpretation A Journal Of Bible And Theology 0-3 (2002).

[6] Skolnik, M., [Radar Handbook, Third Edition], McGraw-Hill, New York, 17.22 (2008). [7] Valenzuela, J.R. and Fessler, J.A., “Regularized estimation of Stokes images from polarimetric measurements”,

Proc. SPIE 6814, 681403 (2008). [8] Gartley, M., Goodenough, A., Brown, S., and Kauffman, R.P., “A comparison of spatial sampling techniques

enabling first principles modeling of a synthetic aperture RADAR imaging platform,” Proc. SPIE 7699, 76990N (2010).

[9] Lee, J.S. and Pottier, E., [Polarimetric Radar Imaging From Basics to Applications], CRC Press, Boca Raton, FL, 302-308 (2009).

[10] Stokes, G.G., “On the composition and resolution of streams of polarized light from different sources,” Transactions of the Cambridge Philosophical Society, Vol.9, 399-416 (1852)



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