IEEE Geoscience and Remote Sensing Magazine - September 2021 - 55

Pavia (OA ..84 32 072 and l 799 0 009!
Pavia1
=
!
=0 .. ), obtained
with the same data set split () employed here, achieved
with a 3D CNN [103], are still inferior to most of our results
given in Table 6.
The reader may note that our classification results differ
from those presented in the original articles of (extended)
APs [19], SDAPs [25], LFAPS [80], and
a - and ~ -APs [56].
More precisely, the differences can be explained by the various
sets of attributes and thresholds employed in some of
the articles [19], [25], [80], the use of pre- and postprocessing
techniques other than PCA [25], and number of RF trees
[25]. Moreover, even using the same set of thresholds and
same number of RF trees, as was done in [56], the quantization
and connectivity parameters, which are not explicitly
given in those articles, may play a role in the final results,
as discussed in the " Assessment of Connectivity and Quantization "
section. Nevertheless, in terms of conclusions,
there is no incoherence between our article and the articles
cited at the beginning of this paragraph.
CLASSIFICATION RESULTS FOR
THE GRAY-POTSDAM DATA SET
The overall and per-class classification results for the Gray-
Potsdam data set using GrayPotsdam1
are presented in
Tables 8 and 9, respectively. As already mentioned, the
reported results are the average scores over 10 runs on
the different random training test splits of
GrayPotsda .m1
Since LFAPs perform better than HAPs in general, as attested
by [80], and due to the expensive computation of
HAPs, we consider only LFAPs in our experiments with
the Gray-Potsdam data set.
In the case of the Gray-Potsdam data set, it can be observed
that AP variants boost accuracy consistently at various
degrees. In particular, the
a -APs and ~ -APs could outperform
APs on each single max-tree or min-tree but still fall below
the standard APs. On the other hand, SDAP performed
better than AP,
a -AP, and ~ -AP. Then, by postprocessing the
output profiles, LFAP and LFSDAP outperformed AP and
SDAP by 3.52% and 4.61%, respectively, in terms of OA.
Among the FPs, the best result was achieved by
FP ,an+ which
outperforms the APs by more than 2% in terms of OA, AA,
and
l . Finally, the TF AP presented lower scores than APs,
but it outperformed AP-maxT, AP-minT, a -AP, and ~ -AP,
despite having the smallest number of dimensions among
all methods. In conclusion, the best classification result was
obtained by LFSDAP, with 80.80% of OA, which represents
an improvement of 5.70% with respect to the standard AP.
Figure 6(a) and (b) presents a crop of the Gray-Potsdam
data set and its ground truth, respectively, composed of the
first 500 lines (from top to bottom) and 1,200 columns
(from left to right) of the original data. Figure 6(c)-(o)
illustrates the classification maps obtained on the crop
of Figure 6(a) using the aforementioned methods. We
can see that the classification based solely on pixel gray
values is very noisy in most regions of the image. By incorporating
spatial information from APs, we see a more
SEPTEMBER 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
55
TABLE 7. THE CLASSIFICATION RESULTS PER CLASS OF THE PAVIA DATA SET OBTAINED BY DIFFERENT METHODS USING THE DEFAULT FOUR-CONNECTIVITY AND 1-B QUANTIZATION.
METHOD
Four PCs
AP-maxT
AP-minT
AP
SDAP
a-AP
~-AP
HAP
HSDAP
LFAP
LFSDAP
FPn
FPa
FPn + a
TF-AP
DIMENSION
4
80
80
152
80
80
80
1,064
340
304
160
152
152
304
72
ASPHALT
71 ..
92 ..
92 ..
95 ..
25 044!
33 014!
81 008!
71 021!
97.15 ± 0.28
89 ..
89 ..
39 021!
73 056!
99.86 ! 0.16
99 ..
90 ..
99 ..
94 ..
95 ..
96 ..
95 ..
7018!
33 09!
42 018!
97 013!
51 025!
03 023!
79 026!
MEADOW
2045!
66 141!
28 442!
38 581!
51 047!
63 043!
70 042!
68 042!
49 046!
23 036!
53 ..
93 ..
80 ..
87 ..
92 ..
96 ..
96 ..
97..
94 ..
96 ..
98.42 ! 0.12
97 ..
73 ..
96 ..
90 ..
1021!
87 22!
61 021!
31 114!
GRAVEL
38 ..
43 ..
86 ..
73 .17 3!
77 ..
76 ..
63 ..
68 ..
72 ..
65..
88 ..
92 ..
92 ..
82 ..
TREE
39 053!
32 067!
02 165!
15 029!
27 11 05!
93.75 ! 7.84
83 171!
59 244!
68 379!
82 051!
65 091!
31 414!
43 128!
42 241!
98 ..
95 ..
98 ..
99 ..
93 ..
99 ..
ACCURACY PER CLASS (%)
METAL
28 01!
61 077!
97 008!
09 029!
21 07!
73 007!
99.75 ! 0.09
97 ..
95 ..
96 ..
92 ..
97 ..
99 ..
97 ..
99 ..
74 011!
25 019!
79 01!
88 08!
07 019!
31 02!
93 043!
64 008!
98 ..
99 ..
99 ..
99 ..
99 ..
99 ..
99..
99 ..
79 017!
63 008!
9008!
65 005!
83 006!
61 007!
64 004!
96 006!
99.99 ! 0.03
99 ..
99 ..
99 ..
99 ..
99 ..
99 ..
2024!
52 018!
89 004!
93 004!
89 004!
75 01!
SOIL
67 ..
71 ..
84 ..
85 ..
99 .08 0!
98 ..
98 ..
80 ..
34 058!
07 024!
19 008!
64 014!
93 006!
95 006!
73 222!
99.68 ! 0.39
98 ..
97 ..
98 ..
86 ..
91 .096!
99 ..
08 009!
06 056!
43 157!
98 118!
23 019!
The values in bold represent the highest scores in each column, i.e., the highest scores achieved for each of the semantic classes of Pavia among all tested methods.
BITUMEN
66 ..
97 ..
99 ..
100 ! 0
98 ..
99 .49 0!
99 .49 0!
99 ..
99..
99 ..
99 ..
100 ! 0
99 ..
99 ..
100 ! 0
BRICK
74 096!
83 014!
93 012!
94 025!
99 003!
55 01!
36 017!
16 014!
98 004!
97 005!
83 ..
95 ..
98 ..
99..
98 ..
99 ..
99 ..
98 ..
99 ..
97 ..
98 ..
97..
28 044!
28 013!
02 013!
24 018!
15 05!
35 01!
36 011!
13 007!
08 006!
28 01!
75 013!
43 053!
99.72 ! 0.1
98 ..
99..
57 038!
61 006!
SHADOW
96 ..
97 ..
93 ..
98 ..
88 ..
97 ..
97 ..
98 ..
89 ..
97 ..
84 ..
64 034!
61 046!
47 301!
25 203!
62 307!
82 044!
12 04!
73 033!
70 248!
12 079!
26 125!
99.92 ! 0.06
97..
98 ..
99 ..
8182!
23 178!
56 006!
IEEE Geoscience and Remote Sensing Magazine - September 2021

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