This document discusses evaluating geometrical parameters of buildings from SAR images. It presents an algorithm developed to retrieve building orientation, height, and double scattering lines. SAR imaging pros and cons are explained. Electromagnetic scattering models for single and double scattering are described. Simulations are shown for 512x512 and ERS-1 C sensors to test the algorithm under different building orientations. The algorithm uses linear regression to determine building orientation from double scattering lines. Conclusions state the algorithm can accurately retrieve parameters given sufficient dots on scattering lines but the range of evaluable angles is limited.

1. UNIVERSITÀ DEGLI STUDI DI NAPOLI “FEDERICO II”
FACOL
TESI DI LAUREA
Evaluation of geometrical parameters of buildings
from SAR images
RELATORE:
CH.MO PROF.
ANTONIO IODICE
CANDIDATO:
FEDERICO MARIA ARIU’
MATR. 528/1127
CORRELATORE:
ING. GERARDO DI MARTINO
ANNO ACCADEMICO 2009/2010

2. Summary
 Introduction and goals
 Models description
 Developed algorithm
 Results

3. 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

4. Geometrical distorsions
 Layover
 Shadowing

5. Electromagnetic diffusion
model
Single scattering

6. Electromagnetic diffusion
model
Double scattering

7. 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

8. 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)

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

10. 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)

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

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

13. 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

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

15. 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

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

17. 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

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

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