IEEE Geoscience and Remote Sensing Magazine - March 2021 - 148

[h Tv1 (x, y), h Tv1 (d 1 (x, y, R 1)), f, h Tv1 (d n (x, y, R 1))
h Tv2 (d 1 (x , y, R 2)), f, h Tv2 (d n (x, y, R 2))
h
h vT M (d 1 (x, y, R M)), f, h vT M (d n (x, y, R M))],
where d j (x, y, R i) is the site with R i distance from (x, y)
along the jth direction.
SURF
SURF defines the local feature by the distribution of the firstorder Haar wavelet response, where the derivative operation
is circumvented by means of an integral image [86], [87].
For image I(x, y), the Haar-like wavelet response is calculated
along the x- and y-axis directions in a circular neighborhood
around the keypoint. The Haar-like wavelet responses within a sliding orientation window covering an angle of r/3
are summed to estimate the dominant orientation. The local descriptor is defined on a square region centered around
the keypoints and oriented along the dominant orientation,

7/ h x, / h y, / h x , / h y A ,
T

where h x and h y are the Haar wavelet responses in the horizontal and vertical directions, respectively.

8

1
8

7

1

7

2

6

3

6

5

4

5

2

3

4
GLOH

R310

R31

R28

R21

R39
R27
R38

R26
R37

R15 R11 R22
R14 R12
R23
R13
R25

R36

R24

R32

R33

R34

R35

AB-SIFT
FIGURE 12. A comparison of GLOH and AB-SIFT. Both the inner

circle and the outer circulars are divided into several sectors for
AB-SIFT. AB: adaptive binning.
148

IMPROVED VERSIONS OF SAR IMAGES
The generic model forms the local descriptor by concatenating the magnitude-weighted orientation histogram in each
cell. The definition of image gradients, therefore, plays a
vital role in representation power. In classical studies, the
image gradients are approximated by differencing the adjacent pixels,

	

Z
-1
]
] fh = f - 2
G x = I ) fh ]
-1
&[
1
G y = I ) fv ]
f
=
f0
] v
]
-1
\

0 1
0 2p
0 1
2 1 , (3)
0 0 p
-2 -1

where G x and G y are the gradients along the horizontal
and the vertical, respectively. The classical definition of
image gradient is applicable to a Gaussian additive noise
environment. As is generally known, the speckle inherent
to coherent radar imaging has the statistical specificity of
multiplicative noise. The correlativity of adjacent pixels in
an SAR image is much stronger than in an optical sensor image. The generic model is, therefore, not effective
for SAR images, as corroborated in the " Experiments and
Discussion " section.
To characterize target scattering signatures from radar
images, it is expected that the interest points located in the
target imaging or radar shadow can be located precisely. The
generated local features can, then, have powerful discrimination ability. Preceding studies on edge detection from
SAR images prove that the impact of speckle and geometric
distortion can be alleviated by the ratio of averages (ROA)
[95]-[99]. The " Conclusion " section provides valuable clues
for interest point detection and local pattern representation
specific to SAR images.
THE ROA
The ROA operator was initially designed for edge detection.
It splits a window centered on the pixel of interest into two
adjacent and nonoverlapping neighbors for four angular
directions, as displayed in Figure 13. The edge was detected by the ROA of adjacent windowed pixels. The ratio of
exponentially weighted averages (ROEWA) operator is an
improved version of the ROA, where the windowed pixels
are further exponentially weighted. Take the horizontal
direction, for example; the windowed pixels on the opposite side are
T 13 =
	

/
/

I (a + x, b + y) w (x, y)

(x, y) ! R t

T 23 =

I (a + x, b + y) w (x, y),



(4)

(x, y) ! Tb

where w (x, y) = exp {< x < + < y < /a} is the weight function;
a is a smooth parameter; and R t and R b denote the top
and the bottom windowed regions, respectively, shown in
Figure 13(c). The edge strengths along the horizontal and
vertical directions are
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

MARCH 2021
IEEE Geoscience and Remote Sensing Magazine - March 2021

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