Analysis of Compact Polarimetric AR Imaging Modes T. L. Ainsworth 1, M. Preiss, N. tacy, M. Nord 1,3 & J.-. Lee 1,4 1 Naval Research Lab., Washington, DC 0375 UA Defence cience and Technology Organisation, Edinburgh, A 5111 Australia 3 Applied Physics Lab., Johns Hopkins Univ., Laurel, MD 073 UA 4 Center for pace and Remote ensing Research, Central National Univ., Taiwan
Compact Polarimetry Enhancing Dual-Pol Imagery Dual-Pol AR Imagery e.g. π/4 Transmit with (H, V) Receive Polarimetric cattering Model Pseudo Quad-Pol Data 1) tandard Quad-Pol Analysis ) Quad-Pol Decomposition 3) Classification, etc.
Compact Polarimetry Enhancing Dual-Pol Imagery Dual-Pol AR Imagery e.g. π/4 Transmit with (H, V) Receive Polarimetric cattering Model Pseudo Quad-Pol Data 1) tandard Quad-Pol Analysis ) Quad-Pol Decomposition 3) Classification, etc. Two Questions: 1) How appropriate is the scattering model? ) What type of dual-pol imagery provides the best input to the scattering model?
Compact Polarimetric Modes / Models Dual-Pol Data Collection Modes tandard Linear Modes: Transmit H (or V) with H & V Receive Not Appropriate for Compact Polarimetry π/4 Mode: Linear Transmit with H & V Linear Receive Circular Transmit Modes: Circular Transmit with Left & Right Circular Receive Circular Transmit with H & V Linear Receive Model imple Natural catterers Reflection ymmetry Assumption Random Volume cattering Model Double-Bounce Correction to Random Volume Model
Compact Polarimetric Modes Dual-Pol cattering Vectors: r T kh = [ HH HV ] r kπ / 4 = HH + HV VV + r T kdc = [ RR RL] r k = + i i + CTLR [ ] T [ ] HH HV π/4 Mode Covariance Matrix [ C ] = [ k ] [ k ] π / 4 π 4 π 4 + = 1 1 VV HH R HH HH VV ( ) HV HH + VV HV HH VV HV HV VV HV T + HH 1 R HV HV HV + VV HV HV ( ) VV HV HV
Reflection ymmetry Assumption Too Many Variables (9), Not Enough Equations (4) Assume Reflection ymmetry HH HV = VV HV = 0 Define a Relationship Between HV and ρ ρ = HH HH VV VV HV + VV ( 1 ρ ) True for a Randomly Oriented Cloud of Dipoles (Volume cattering), but HH = 4
DLR E-AR Imagery Quad-Pol Data to imulate Compact Polarimetric Modes Pauli Display Red: HH-VV Green: HV Blue: HH+VV L-band Imagery of Oberpfaffenhafen
Test of HV vs. ρ Relationship A catter Plot of vs. HH HV + VV 1 4 ( 1 ρ ) hows a Possible Problem. ( 1 ρ ) 4 (All points should lie on the diagonal line.) HV HH + VV
Double-Bounce Correction A Useful Mathematical Inequality: ( ) ( ) ρ + 1 HH VV HH VV Rewriting Yields ( ) + HH HV VV ( 1 ρ ) HH HV VV HH - VV / HV is the Double-Bounce Correction First Estimate the HH - VV / HV Ratio Then Apply this New Relationship
Use the Original Compact Polarimetry Model to Estimate the HH - VV / HV Ratio. Model Improvement Use this Estimate to Determine the Ratio of HH HV + VV HH VV To ( 1 ρ ) And olve for the Pseudo Quad-Pol Data ( 1 ρ )( HH + VV )
π/4 Mode vs. Quad-Pol
π/4 Mode vs. Quad-Pol
CTLR Mode vs. Quad-Pol
CTLR Mode vs. Quad-Pol
Pseudo Quad-Pol Comparison Original Quad-Pol Imagery Red: HH-VV Green: HV Blue: HH+VV π/4 Mode Compact Polarimetric Imagery Dual-Circ Compact Polarimetric Imagery Circ X-mit / Linear Rec. Compact Polarimetric Imagery
Graphic Dual-Pol Analysis Dual-Pol Receives Two Orthogonal Polarizations Can ynthesize Any Receive Polarization, in Principle Ellipticity and Orientation Fully Characterize the Polarization of the Received ignal Dual-Pol Decompositions Entropy is Entropy, but Alpha Angle No Longer Just a cattering Mechanism b a tan χ = b a
Linear Dual-Pol ignatures Linear Horizontal Transmit Polarization Dihedral Response urface Response
π/4 Dual-Pol ignatures Linear π/4 Transmit Polarization Dihedral Response urface Response
Dual-Pol Circular ignatures Right-hand Circular Transmit Polarization Dihedral Response urface Response
Dual-Pol Vegetation ignatures H Transmit Looks like the Dihedral and urface Plots! π/4 Transmit Looks like the urface Plot.
Dual-Pol Vegetation ignatures H Transmit Looks like the Dihedral and urface Plots! Right-hand π/4 Transmit Circular Looks This like one the is urface Different. Plot.
Circular-Transmit, Dual-Pol Conclusions Circular Dual-Pol eparates catterers Dihedrals, Rough urfaces, Dipoles, Vegetation ignature Plots Differ for These catterers Circular Does Not Detect Target Orientation Except for ingle Dipole catterers Extracting Terrain lopes May be Difficult Without an Orientation Angle Response
Example of Dual-Pol Imagery PIAR X-band Imagery, Tsukuba, Japan Quad-Pol Imagery Pauli Basis Display Dual-Pol Display
Example of Dual-Pol Imagery PIAR X-band Imagery, Tsukuba, Japan Quad-Pol Imagery Pauli Basis Display Dual-Pol Display
Ingara Quad-Pol X-Band Dataset Quad-Pol tandard Display: Hue: α-angle at.: Entropy Value: pan
(HH, HV) Dual-Pol Imagery Dual-Pol Display: Red: HH Green: HV Blue: HH HV
Rotated Dihedral catterer Linear Horizontal Transmit Polarization Unrotated Dihedral 30º Rotated Dihedral
Rotated Dipole catterer Linear Horizontal Transmit Polarization Unrotated Rotated 30º
Rotated urface catterer Linear Horizontal Transmit Polarization Unrotated urface 30º Rotated urface
H Transmit, Dual-Pol Information Linear Dual-Pol Can Distinguish Between Rotated Dihedrals (or Dipoles) Rough urfaces (Trihedrals) Randomly Oriented Dipole Distributions Typical Vegetation Models Linear Dual-Pol Cannot Distinguish Between Dihedrals and Dipoles, Either Rotated or Not Unrotated Dihedrals (or Dipoles) and Any Rough urface
Linear Dual-Pol Decomposition Eigen Decomposition of the x Covariance Matrix C C HH, HH HV, HH C C HH, HV HV, HV cosα1 = sinα1 e α λ1 Define Angle and Entropy as α = λ α + ιϕ = cosα sinα e ιϕ cosα1 λ cosα ( π ) 1 1 λα λ1α 1 λ α1 + sinα e 1 sinα e ιϕ ιϕ ( λ lnλ + λ ln ) ln Entropy = 1 1 λ with ( ) λ i = λ i λ 1 + λ
H Transmit, Dual-Pol Entropy-Alpha Plot Allowed Dual-Pol α / Entropy Region Blue: urface cattering Green: Vegetation Random Dipole Distribution Cyan: Vegetation urface Mix Red: ingle Dipoles or Double Bounce Magenta: Dihedral urface Mix Yellow: Dihedral Vegetation Mix White: High Entropy Low Polarimetric Content Orange: Rotated Dihedral / Dipole Mix, HV > HH with HH HV ~ 0
Linear Dual-Pol Decomposition (HH, HV) Dual-Pol Imagery Hue: α-angle at.: Entropy Value: pan
ummary Compact Polarimetry Results Depend Upon: The Reflection ymmetry Assumption An Appropriate cattering Model Matched to the Transmitted Polarization The Double-Bounce Correction Appears to Give Fairly Good, Robust Results Dual-Pol ignature Plots: Complete Polarimetric Description of Dual-Pol Imagery Provides a imple, Visual Analysis Technique Dual-Pol Decompositions: Alpha Angle Not Just the cattering Mechanism Any More Interpretation of Dual-Pol Alpha-Entropy Plots Depends Upon the Transmitted Polarization
Dual-Circular Mode vs. Quad-Pol
Dual-Circular Mode vs. Quad-Pol
Polarimetric Covariance Matrix Rearranging complex elements of the scattering matrix, The covariance matrix is formed by u = [ C] = u u T = Hermitian matrix, positive semi-definite Real positive eigenvalues For statistical analysis, speckle filtering and classification, the covariance matrix is preferred.
Polarimetric Covariance Matrix Rearranging complex elements of the scattering matrix, The covariance matrix is formed by u = [ C] = u u T = Hermitian matrix, positive semi-definite Real positive eigenvalues For statistical analysis, speckle filtering and classification, the covariance matrix is preferred.
Polarimetric Covariance Matrix Rearranging complex elements of the scattering matrix, The covariance matrix is formed by u = [ C] = u u T = Hermitian matrix, positive semi-definite Real positive eigenvalues For statistical analysis, speckle filtering and classification, the covariance matrix is preferred.
Polarimetric Covariance Matrix Rearranging complex elements of the scattering matrix, The covariance matrix is formed by u = [ C] = u u T = Hermitian matrix, positive semi-definite Real positive eigenvalues For statistical analysis, speckle filtering and classification, the covariance matrix is preferred.
Quad-Pol Entropy / Alpha pace Low Medium High MULTIPLE CATTERING VOLUME CATTERING URFACE CATTERING
Linear Dual-Pol Decomposition (VV, VH) Dual-Pol Imagery Hue: α-angle at.: Entropy Value: pan
Linear Dual-Pol Decomposition (VV, VH) Dual-Pol Imagery Hue: VV VH at.: Entropy Value: pan
Linear Dual-Pol Decomposition (HH, HV) Dual-Pol Imagery Hue: HH HV at.: Entropy Value: pan