IEEE Geoscience and Remote Sensing Magazine - September 2021 - 63

baseline results by 20.21-31.49% in terms of OA, while, with
Pavi ,a2
the improvement ranges from 1.65% to 15.99%.
Moreover, with Pavi ,a2 as shown in Table 14, none of
the AP-based methods outperforms the baseline with respect
to the brick class, and we observe a less remarkable
improvement for the meadow class. On the other hand, the
best scores achieved with Pavia2
for the other seven classes
are comparable with the best scores obtained for Pavi .a1
For the Pavia data set, we can conclude that the classification
results with AP-based methods presented in the " Experimental
Study " section cannot be generalized to more
realistic scenarios (with better separation between training
and test pixels). In fact, it appears that APs are much less
useful when the training and test samples belong to regions
with dissimilar spatial and geometric properties. For instance,
the training and test pixels of the asphalt class all
belong to thin and elongated regions, which may be why
the results for this class are improved by all AP-based methods
with respect to the baseline. On the other hand, the
pixels in the training and test sets of the meadow class belong
to components with very different shapes, which may
partially explain the worse results on this class.
Figure 8(d)-(n) illustrates the classification results
of Table 13. We can observe that all AP-based methods
considerably improve the classification results of the bare
soil class (in light green) with respect to the baseline results
[Figure 8(d)]. This can be due to the training and
test pixels sharing nodes/features at higher levels of the
trees. On the other hand, the classification results of the
shadow and meadow classes are worsened by at least half
of those methods.
We now compare the results between the partitions
GrayPotsdam1
and GrayPotsdam2 of the Gray-Potsdam data
set. Table 15 presents the classification results obtained with
the partitions GrayPotsdam1
(already given in Table 8) and
GrayPotsda .m2 Similarly to Pavia, we can observe a significant
drop in classification accuracy for all AP-based methods
when the new partition GrayPotsdam2
is used. While
APs improve the baseline scores by up to 31.38% on the
GrayPotsdam1
partition, the classification improvements
do not exceed 10.55% on the new partition GrayPotsda .m2
Moreover, the classification results of two of the six classes
(low vegetation and impervious surfaces) are worsened by
most of the AP-based methods, as shown in Table 16.
Figure 10(d)-(n) illustrates the classification results on
the crop of Gray-Potsdam given in Figure 10(b) [the same
as Figure 6(b)] obtained with the partition
GrayPotsda .m2
The regions of the cropped image, which contributed to
the training set of
GrayPotsda ,m2 are shown in Figure 10(c).
Our main observation is that the classification results of
the regions that do not contribute to the training sets are
much poorer if compared to other regions of the same
class. For instance, among the pixels belonging to the largest
CC of the impervious class (which does not contribute
to the training sets), virtually no pixels are correctly classified
by the tested methods. In contrast, the pixels of this
SEPTEMBER 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
63
TABLE 14. THE CLASSIFICATION RESULTS PER CLASS OF THE PAVIA DATA SET PERFORMED ON THE PARTITION PAVIA2 [FIGURE 8(B) AND (C)].
METHOD
Four PCs
AP-maxT
AP-minT
AP
SDAP
a-AP
~-AP
FPn
FPa
FPn + a
TF-AP
DIMENSION
4
80
80
152
80
80
80
152
152
304
72
ASPHALT
82 ..
95 ..
92 ..
97 ..
34 097!
06 134!
49 08!
5134!
98.34 ± 0.44
95 ..
95 ..
96 ..
95 ..
96 ..
95 ..
71 055!
65 041!
86 093!
33 121!
32 134!
72 059!
MEADOW
41 ..
30 ..
49 ..
35 ..
69 149!
95 13!
23 613!
74 282!
64.6 ± 8.24
02 047!
58 325!
86 252!
76 282!
13 658!
59 11 73!
43 ..
41 ..
60 ..
40 ..
53 ..
45 ..
The values in bold represent the highest accuracy scores in each column.
GRAVEL
44 ..
87 ..
86 ..
92 ..
89..
32 ..
32 ..
98 ..
99 ..
62 ..
TREE
88 267!
22 268!
24 802!
41 409!
62 695!
89 004!
89 007!
62 114!
53 049!
99.84 ± 0.09
79 658!
98 ..
98 ..
98 ..
98 ..
96 ..
ACCURACY PER CLASS (%)
METAL
09 029!
25 019!
64 021!
85 017!
04 039!
99.1 ± 0.18
99 ..
98 ..
98 ..
98..
98 ..
06 019!
94 015!
85 02!
88 016!
99 015!
98 ..
99 ..
99 ..
99 ..
99 ..
99..
99 ..
99 ..
99 ..
43 047!
7011!
33 039!
69 011!
44 02!
1025!
15 028!
7013!
68 017!
99.73 ± 0.11
99 ..
69 012!
SOIL
59 ..
94 ..
97 ..
98 ..
82 18!
68 075!
61 046!
34 087!
99.34 ± 0.19
98 ..
98 ..
96 ..
98 ..
98..
98 ..
56 016!
39 03!
41 088!
88 035!
28 04!
72 027!
BITUMEN
75 ..
97 ..
99 ..
100 ± 0
99..
99 ..
99 ..
100 ± 0
100 ± 0
100 ± 0
100 ± 0
59 321!
43 042!
9009!
71 034!
5003!
51 006!
BRICK
60.84 ± 3.01
23 016!
2021!
45 045!
16 003!
13 10 79!
09 146!
17 237!
3453!
7447!
70 91!
37 ..
38 ..
37..
37 ..
41 ..
38 ..
38..
41..
40..
58..
SHADOW
99..
99 ..
57 ..
96 .605!
54 ..
75 ..
67 ..
78 .65 17!
59 ..
58 ..
28 016!
9015!
41 114!
16 013!
18 171!
01 705!
01 131!
63 176!
99.95 ± 0.08
IEEE Geoscience and Remote Sensing Magazine - September 2021

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