terms of over- and under-segmentation error ratios and scale-
parameter dependency. Given that the same experimental
data as those in Wang and Li (2014) were used, we mainly
conducted comparisons of the refined and original
HBC-SEG
methods in the present study. Segmentation at multiple scales
and different spectral weights before and after the improve-
ments was conducted. Method accuracy, scale-parameter
dependency, and efficiency were compared quantitatively
and qualitatively. To clearly demonstrate the advantages of
the refined method, the segmentation results of
HBC-SEG
and
FNEA
at large scales without straight line constraints were also
presented and analyzed.
Tuning of Method Inputs
Compared with the original version, the refined method
requires an additional input,
T_SL
. This input is influenced
by remote sensing image types, resolutions, and application
requirements; hence, specifying a fixed constant value or
range is difficult. Generally,
T_SL
should be at least larger
than
T_scale
used in the non-constrained merging of
HBC-SEG
;
otherwise, the refinement step would not function. In addi-
tion,
T_SL
should be equal to or slightly larger than
T-scale
,
which could merge the expected over-segmented object cate-
gories for the non-constrained merging in
HBC-SEG
. A practical
means to determine a suitable
T_SL
is to create a segmenta-
tion hierarchy from a small scale to a large scale through
HBC-
SEG
in several testing areas and visually estimate the over- and
under- segmentation errors in the ground objects of interest.
In our experiments,
T_SL
was estimated as 50 through visual
interpretation on scales 10 to 80 obtained by
HBC-SEG
with
a step of 10 because reducing over-segmentation errors in
man-made objects, such as buildings, is our main goal. Other
inputs less or larger than 50 are also possible with changes
in the over- and under-segmentation error ratios. For the
inputs used in
IPSL
-neighborhoods,
T
1
is equal to 0.90 for the
unilateral and tangent relationship of segments;
T
2
is equal
to 15, which implies that straight lines shorter than 15 pixels
are not considered; and
T
3
is equal to 3.0, indicating that the
projected lengths of segments need to be less than three times
their contained and touched straight lines. These inputs were
specified after several rounds of sample testing and were used
as uniform default inputs in all the experiment analyses.
HBC-SEG
requires inputs, such as
T_scale
, weight of spectral
heterogeneity
w
, and weight of compact heterogeneity
w
cmpct
.
Input
w
should preferably be larger than 0.5 to allow the
merging criterion to be dominated by spectral heterogeneity
and to guarantee visually appealing segmentation results.
The influence of
w
cmpct
on segmentation is small compared
with that of
T_scale
and
w
. Input
T-scale
was generally set to
a relatively small value because the segments were merged
adequately in edge-constrained merging in
HBC-SEG
. We tested
scales 10 and 20. In each scale, we decreased
w
from 1.0 (only
spectral heterogeneity was considered) to 0.9 and stopped at
0.7;
w
cmpct
was fixed at 0.5. Further information on these in-
puts is presented in the studies of Baatz and Shäpe (2000) and
Wang and Li (2014). We first obtained the reference segmenta-
tion results by visual interpretation and then calculated the
segmentation accuracy of both methods for each parameter
combination scheme. In experimental area 1, we integrated
several trees and their neighboring grasslands into single seg-
ments for two reasons: (a) we mainly focused on man-made
objects, and the method was mainly designed to reduce inner
over-segmentation errors, and (b) in areas where it is difficult
to distinguish clear boundaries between two types of ground
objects, the blunt delineation of such boundaries might result
in an unfair evaluation of different segmentation methods.
Method Accuracy Measures
We used the numeric measures employed by Carleer
et al
.
(2005), Crevier (2008), and Yi
et al
.
(2012). The best matching
function of a region is defined as follows:
l
(
i
) = arg max
j
S S
S S
i
m
j
h
i
m
j
h
∩
∪
.
(10)
Segmentation precision
p
, recall ratio
r
, and measure
m
2
are formulated as follows:
p
=
S S
A
i
m
l i
h
i
n
m
∩ ∑
=
( )
1
,
(11)
r
=
1
1
A
S
S S
S
i
m i
m
l i
h
l i
h
i
n
m
∩
∑
=
( )
( )
,
(12)
m
A
S
S S
S S
i
n
i
m i
m
l i
h
i
m
l i
h
m
2
1
1
=
=
∑
∩
∪
( )
( )
.
(13)
In Equations 10 through 13,
S
i
m
denotes segment
i
in the
segmentation image,
S
j
h
denotes object
j
in the reference map,
n
m
is the segment number, and
A
is the summed area of all
segments. Measure
p
denotes the degree of segments con-
tained in a reference map. If segments are fully contained by
the reference map, e.g., one-pixel segmentation,
p
is equal to
1.0. Thus,
p
measures under-segmentation errors. Measure
r
reflects the degree of segmentation covering reference objects.
When
p
and
r
are both equal to 1.0, segmentation fully coin-
cides with the reference map. Measure
m
2
balances the influ-
ence of over- and under-segmentation errors. These measures
are within [0, 1], and large measures are preferred.
Experimental Analyses
Method Accuracy
Since its publication,
HBC-SEG
method has undergone several
minor step modifications and improvements, including those
in gradient calculation and
OP
output. The differences in
visual effects and quantitative accuracy assessment are shown
in Plates 1 to 3 and Table 2 in this paper and in Figures 6, 7,
and 9 and Table 2 in our previous study (Wang and Li, 2014).
The quantitative results are presented in Table 2. Measure
p
decreased from scale 10 to 20, and measure
r
increased in both
methods. These results indicate an increase in under-segmen-
tation error and a reduction in over-segmentation error with
the increase in scale. Such results are reasonable for region-
merging-based methods. At the same scales, measure
r
im-
proved after method refinement. In the first experimental area,
measure
r
exhibited an average increase of 0.048 (scale 10) and
0.042 (scale 20). In the second area, the average increase was
0.041 (scale 10) and 0.036 (scale 20). These observations cor-
respond with our objectives. Considering the remerging step,
measure
r
was expected to increase (over-segmentation error
decreased). The key is that the increase in
r
should not cause
under-segmentation errors; otherwise, such decrease in over-
segmentation errors would be unfavorable. In the first area,
measure
p
exhibited an average decrease of 0.006 at scales
10 and 20; in area 2, the reductions were 0.004 (scale 10) and
almost 0 (scale 20). These results indicate that most of the
segments that re-merged in the refined method were over-seg-
mented and thus caused very small merging errors. Measure
m
2
, as a balanced index to evaluate method accuracy, increased
in the refined method. In the first area, measure
m
2
increased
by 0.038 at scale 10 after refinement and by 0.029 at scale 20.
In the second area, the increase was 0.031 (scale 10) and 0.037
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