IEEE Geoscience and Remote Sensing Magazine - December 2023 - 16

ab
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θ∈ [-90,0)
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θ∈ [-90,0)
x-Axis
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FIGURE 7. A visualization of the five-parameter representation and eight-parameter representation
methods for rotated objects [106]. (a) Five-parameter representation with 90°
angular range. (b) Five-parameter representation with 180° angular range. (c) Eight-parameter
representation.
angle classification representation [106], [127], [128],
[129], Gaussian distribution representation [130], [131],
[132], [133], and others [134], [135], [136], [137], [138], [139],
[140], [141], [142], [143], [144].
FIVE PARAMETERS
The most popular solution is representing objects with a
five-parameter method (, ,, ,),xywh i which simply adds an
extra rotation angle parameter i on the HBB [107], [108],
[109], [110], [111], [112], [113], [114], [115]. The definition
of the angular range plays a crucial role in such methods,
where two kinds of definitions are derived. Some studies
[107], [108], [109], [110], [111], [112] define i as the acute
angle to the x-axis and restrict the angular range to 90°, as in
Figure 7(a). As the most representative work, Yang et al. [107]
followed the five-parameter method to detect rotated objects
and designed an intersection-over-union (IOU)-aware
loss function to tackle the boundary discontinuity problem
of rotation angles. Another group of works [113], [114],
w h ab
Step 1
b
w
w
h
X h
Step 2 a
θ
Y
(a)
d
Y
(b)
FIGURE 8. The boundary discontinuity challenge of the (a) fiveparameter
method and (b) eight-parameter method [119], [121].
16
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ab
d
b
[115], [116] refers to i as the angle
between the x-axis and the long side,
whose range is 180°, as in Fig ure 7(b).
Ding et al. [114] regressed rotation
angles by five-parameter methods
and transformed the features of horizontal
regions into rotated ones to
facilitate rotated object detection.
EIGHT PARAMETERS
Differing from five-parameter methods,
eight-parameter methods [117],
[118], [119], [120], [121], [122], [123],
[124], [125], [126] solve the issue of
rotated object representation by
directly regressing four vertices,
,, ,, ,, ,,
aa bb cc dd
xy xy xy xy
" ^^ ^^hh hh, as
described in Figure 7(c). Xia et al.
[117] first adopted the eight-parameter
method for rotated object representation,
which directly supervises
the detection model by minimizing
the difference between each vertex
and the ground truth coordinates during training. However,
the sequence order of these vertices is essential for the
eight-parameter method to avoid unstable training. As evident
in Figure 8, it is intuitive that regressing targets from
the red dotted arrow is an easier route, but the actual process
follows the red solid arrows, which causes the difficulty
of model training. To this end, Qian et al. [119], [121] proposed
a modulated loss function that calculates the losses
under different sorted orders and selects the minimum case
to learn, efficiently improving the detection performance.
ANGLE CLASSIFICATION
To address the issue present in Figure 8, many researchers
[106], [127], [128], [129] take a detour from the boundary
challenge of regression by transforming the angle prediction
problem into an angle classification task. Yang et al.
[106] proposed the first angle classification method
for rotated object detection, which converts the continuous
angle into a discrete kind and trains the model with
novel circular smooth labels. However, the angle classification
head [106] introduces additional parameters and
degrades the detector's efficiency. To overcome this, Yang
et al. [129] improved the work in [106] with a densely
coded label that ensures both the accuracy and efficiency
of the model.
GAUSSIAN DISTRIBUTION
Although the preceding methods achieve promising progress,
they do not consider the misalignment between the actual
detection performance and optimization metric. Most
recently, a series of works [130], [131], [132], [133] aim to
handle this challenge by representing rotated objects with a
Gaussian distribution, as detailed in Figure 9. Specifically,
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IEEE Geoscience and Remote Sensing Magazine - December 2023

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