IEEE Geoscience and Remote Sensing Magazine - March 2021 - 145

invariance to pose, configuration, and incidence angle change
as well as geometric distortions should be further studied.
KEYPOINT-BASED LOCAL DESCRIPTORS
Recent developments in machine learning prove that local
region description could produce powerful cues for feature
representation. Compared to holistic features, a keypointbased local descriptor is much more robust to local distortion and intensity change. This article attempts to characterize target signatures with local descriptors. We review
state-of-the-art studies in the literature.
KEYPOINT DETECTION
The interest points are first searched by checking image
patterns that differ from the immediate neighborhood.
The fashion of representation could yield a high repeatability, i.e., the keypoints can be extracted reliably and are
often found again at similar locations in other images of
the same object or scene. The typical approaches are described as follows.
DIFFERENCE OF GAUSSIAN
A difference of Gaussian (DoG) detector builds a Gaussian scale space S (x, y, v) by convolving image I(x, y) with a
Gaussian low-pass filter G (x, y, v) parameterized by a standard deviation v [82],
S (x, y, v s) = G (x, y, v s) ) I (x, y),
where v s is a function of index s = {0, 1, f, s max-1}. A DoG
image is the difference between two successive layers:
D (x, y, v s) = S (x, y, v s + 1) - S (x, y, v s).

HARRIS OPERATORS
The Harris corner detector is based on the eigenvalues of
the second-moment matrix (autocorrelation). Candidates
with low contrast are filtered by thresholding the values of
the generated matrix,

TABLE 6. TYPICAL STATISTICS FEATURES.
STATISTICS FEATURES

REFERENCES

Logarithm cumulant

[65]-[67]

Zernike moment

[68], [69]

Chebyshev moment

[70]

Krawtchouk moment

[71]

Low-order moment

[72]

TABLE 7. TYPICAL ELECTROMAGNETIC SCATTERING FEATURES.
ELECTROMAGNETIC SCATTERING FEATURES

REFERENCES

Point scattering center model

[73]

Damped exponential model

[74]

Prony's scattering center model

[75], [76]

GTD scattering center model

[77], [78]

Attributed scattering center model

[79], [80]

(3D) global scattering center model

[81]

GTD: geometrical theory of diffraction.

Scale

Gaussian

Image pyramids are then built to achieve scale invariance. The number of octaves is determined by the size of
the image. The higher-order-octave image is obtained by

down-sampling the image of the previous octave by a factor
of two. The keypoint is defined as the local extrema in 3D
space (x, y, v). Each pixel is compared to the eight neighboring pixels in the current scale and the nine neighboring
pixels in the scales above and below. If a pixel is larger or
smaller than all of its neighbors, it is accepted as a preliminary keypoint candidate, as pictorially shown in Figure 8.

DoG
Space
26-Neighbor

FIGURE 8. A DoG detector. The pixel (in red) is compared to the eight neighbors in the current scale and the nine neighbors in the previous

and next scales.
MARCH 2021

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IEEE Geoscience and Remote Sensing Magazine - March 2021

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