IEEE Geoscience and Remote Sensing Magazine - December 2021 - 199

with a 1-ft/pixel resolution. The data set contains highly
overlapping classes and has 100 images per class; examples
appear in Figure 6(a). We extracted 33 3## color patches
from each image, which yielded 6,499,950 27-dimension
feature vectors per class. Then, we developed a Gaussianization
transformation for each class and computed the
(spatiospectral) T using RBIG; see Figure 6(d). We show
in Figure 6(e) the average and standard deviation of the T
evolution through 50 iterations for the 21 classes (note the
log scale) and the total correlation per class. More textured
classes, such as runaways, freeways, buildings, and intersections,
lead to higher T, while rather homogeneous/flat
(a)
g11 g12 g13
b12 b13
b11
r11 r12 r13
r21 r22 r23
r31 r32 r33
(b)
5
-5
15
-10
-15
-20
-25
-30
-35
0102030
Iterations
(d)
40
10
5
50 02 46 810
(e)
T
FIGURE 6. The estimation of the total correlation, T, in very-high-resolution aerial imagery. (a) Images for each of the 21 classes in the database,
ranked according to their estimated T. (b) Each image is decomposed in 33# patches with three channels (red-green-blue), making
samples of 27 dimensions. (c) We measure how much overlap there is between the information content (i.e., the total correlation) of the 27
dimensions for each class. We show a Venn diagram to illustrate the measured information, following the same criteria as in Figure 3. (d) The
average total correlation is iteratively computed for the different 21 class-specific RBIG models through 50 iterations, with the mean T (solid)
and the T standard deviation (shaded) across all models. Convergence is achieved very rapidly for all classes (note the log scale). (e) The
ranked T per class computed from the RBIG models [78].
DECEMBER 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
199
20
Parking Lots
Runways
Airplanes
Buildings
Freeways
Beaches
Sparse Residential
Intersections
Agriculture
Dense Residential
Overpasses
Rivers
Storage Tanks
Baseball Diamonds
Harbors
Medium Residential
Tennis Courts
Mobile Home Parks
Golf Courses
Forest
Chaparral
22
32
g23
g33
22
32
b23
b33
g11
r11
r21
r31
r32
T
g33
r33
(c)
b11
b12 b13
b23
b33
log (T)
Forest
Chaparral
Agriculture
Mobile Home Parks
Sparse Residential
Golf Courses
Airplanes
Beaches
Rivers
Harbors
Tennis
Parking Lots
Medium Residential
Storage Tanks
Dense Residential
Baseball Diamonds
Intersections
Buildings
Freeways
Overpasses
Runways

IEEE Geoscience and Remote Sensing Magazine - December 2021

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - December 2021

Contents
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