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Information about Evaluation of geometrical parameters of buildings from SAR images

The aim of this study is to develop a tecnique able to support the retrieval of the buildings height from SAR images.

In particular, an automatic method, which allows to evaluate the orientation angle of buildings in respect to the projection on the ground of the flight line of the radar platform, has been developed.

The starting point was the algorithm output that allows to identify and extract from SAR images the double scattering contribution whose intensity is linked to the geometrical and electromagnetic parameters of the buildings.

On SAR images, the double scattering contributions turn out to be misaligned dots, so, before evaluating the slope of the straight line of double scattering, a linear regression operation was necessary, starting from the knowledge of the coordinates of each pixel belonging to the line of double scattering.

Given the prospective presence of outliers, the absolute deviation instead of the standard deviation has been used.

In particular, an automatic method, which allows to evaluate the orientation angle of buildings in respect to the projection on the ground of the flight line of the radar platform, has been developed.

The starting point was the algorithm output that allows to identify and extract from SAR images the double scattering contribution whose intensity is linked to the geometrical and electromagnetic parameters of the buildings.

On SAR images, the double scattering contributions turn out to be misaligned dots, so, before evaluating the slope of the straight line of double scattering, a linear regression operation was necessary, starting from the knowledge of the coordinates of each pixel belonging to the line of double scattering.

Given the prospective presence of outliers, the absolute deviation instead of the standard deviation has been used.

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Summary Introduction and goals Models description Developed algorithm Results

SAR images Pros: • Image quality not depending on: Solar illumination Weather trends • Wide coverage area • High resolution Cons: • Need of processing data to obtain the image

Geometrical distorsions Layover Shadowing

Electromagnetic diffusion model Single scattering

Electromagnetic diffusion model Double scattering

EM scattering from buildings BW=Backscattering from Wall BR= Backscattering from Roof BG=Backscattering from Ground D= Double scattering T= Triple scattering Lr =Range size of Layover Sr =Range size of Shadow S= Shadow

Scattering model Double scattering 0 hl tan cos k 4 2 2 S pq 1 tan 2 sin 2 4 k cos 4 r 2 0 E0 2 ES 2 1 2 2 exp tan C ' ' (0) 2 2 θ: detector angle φ: building orientation angle in respect to the detector azimuth k: propagation constant σ2: standard deviation h: buildings height l: buildings length Spq: scattering matrix 2 2 sin 2 2 C ' ' (0)

Evaluation of orientation angle:usefulness Geometrical knowledge Geometrical and electromagnetic parameters retrieval

Height retrieval Geometrical method: h Lr h cos S r cos : Radiometric method h 0 a b 4 a k 2 where b l tan 2 S pq cos 1 tan 2 2 sin 4 k cos 2 2 1 2 2 C ' ' (0) exp tan 2 2 sin 2 2 C ' ' (0)

Double scattering line retrieval Scanning equiazimuth ith row M Ideal sinc Zero-Padding correlation Retrieval of maxima

Double scattering line analysis y=mx+q m=tanα The software returns coordinates and intensity of the dots forming the double scattering line.

Linear regression Yi Xi Given a cloud of sampled dots, the linear regression supplies the straight line that rounds best the trend of the cloud of dots. ui

Choosing the linear regression algorithm The chosen algorithm minimizes minimizza lo scarto assoluto. ABSOLUTE DEVIATION y x STANDARD DEVIATION

SAR images simulations: 512 x 512 SENSOR OVERVIEW Platform height h = 20 Km Platform speed v = 0.9 Km/s View angle θ = 28° Antenna dim(azimuth) L x SAR 8 .5 m Antenna dim (range) L rSAR 1 .5 m Carrier frequency f = 1.282 GHz Pulse duration τ = 1.9 μs Chirp pulse bandwidth Δf = 14 MHz Sampling frequency fsamp = 31 MHz Pulse repetition frequency p.r.f. = 350 Hz Azimuth resolution Δx = 2.5714 m Range resolution Δy = 10.3067 m

SAR images simulations: 512x512 sensor Simulation 1: φ = 10 φs = 15.0° Simulation 2: φ = 25 φs = 26.6°

SAR images simulations: ERS-1 C SENSOR OVERVIEW Platform height h = 775 Km Platform speed v = 6.7 Km/s View angle θ = 23° Antenna dim(azimuth) L x SAR 11 . 1 m Antenna dim (range) L rSAR Carrier frequency f = 5.3 GHz Pulse duration τ = 37.1 μs 1 .0 m Chirp pulse bandwidth Δf = 15.55 MHz Sampling frequency fsamp = 18.98 MHz Pulse repetition frequency p.r.f. = 1.68 kHz Azimuth resolution Δx = 3.9860 m Range resolution Δy = 19.9285 m

SAR images simulations: ERS-1 C sensor Simulation 1: φ = 10 φs = 10.1° Simulation 2: φ = 30 φs = 30.0°

Conclusions Pros: • Good accuracy depending on the numbers of dots that belong to the line. Cons: • Range of angles to be evaluate low.

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