Geoscience Reference
In-Depth Information
METHODOLOGY
Radiometric Normalization and Geometric Correction
Both images were first geometrically corrected into Universal Transverse Mercator
(UTM) projection using first order polynomials and appropriate Ground Control
Points (GCP) collected from topographic maps. Then, radiometric normalization was
employed using a histogram matching algorithm.
Fourier Transform
Any one-dimensional function,
f(x)
(which might be a row or column of pixels), can
be represented by a Fourier series composed of some sine and cosine terms and their
associated coefficients combination. Different spatial frequencies over an image can
be represented by many sine and cosine terms and with their associated coefficients.
Fourier series are effective to identify and quantify spatial frequencies (Erdas Field
Guide, 2005; Gonzalez and Wintz, 1977). Since an earthquake changes the spatial
structure of a related area because of collapsed or damaged buildings, roads, and so on,
Fourier series can be used to identify different spatial frequencies in images obtained
before and after the earthquake which indeed lead information about the earthquake-
induced damages.
The FFT calculation used in this research is shown in the equation 1 (Erdas Field
Guide, 2005):
M
1
∑
−
N
1
∑
−
j
2
π
ux
j
2
π
vy
⎡
⎢
⎤
⎥
(
←
()
Fu
,
v
fx
,
y
e
−
(1)
M
N
x
=
0
y
=
0
where:
M
= the number of pixels horizontally
N
= the number of pixels vertically
u,v
= spatial frequency variables
e
= 2.71828, the natural logarithm base
j
= the imaginary component of a complex number
Once the FFT is applied, a raster image from the spatial domain is converted into
a frequency domain image. The Fourier image can be edited (mainly using fi lters) to
reduce noise, to identify specifi c features or to remove periodic features. After edit-
ing the Fourier image, it is transformed back into spatial domain using IFFT equation
(equation 2) (Erdas Field Guide, 2005):
M
1
∑
−
1
∑
N
−
1
N
1
N
2
j
2
ux
M
π
j
2
π
vy
⎡
⎢
⎤
⎥
(
←
()
fx
,
y
Fu
,
v
e
+
(2)
N
u
=
0
v
=
0
0
≤
x
≤
M
−
1, 0
≤
y
≤
N
−
1
Difference Image and Level Slicing
A difference image was calculated by subtracting the inverse Fourier transformed
post- and pre-earthquake images. The difference image then divided into slices based
on the number of bins (10 for this research) using the following equations:
