IEEE Geoscience and Remote Sensing Magazine - June 2016 - 47

acquisitions, in which the spectra are spatially detrended
using Gaussian processes to avoid shifts related to localized class variability. In [49], the authors perform anomaly detection by a sparse discriminative transform that
maximizes the distance between the anomaly class and
the background classes (defined as a set of endmembers)
and minimizes the distance between the source and target
distributions after reduction by PCA. In [50], the authors
consider the domains as multidimensional graphs and
propose to align the domains by solving a graph-matching
problem. Finally, the authors in [51] find a multispectral
mapping between source and target spectra to project the
labeled pixels of the source domain into the target domain.
Tie points are found between the labeled source pixels and
the pixels in the target by registration, and then the mapping between the source and target is learned by regression
between the corresponding pairs. Then the labeled pixels
are projected into the target domain and are used to train
a classifier therein. As for [40], partial overlap between the
images is required.
As one can see in Table 1, some methods will be more
suitable than others, depending on the problem. For example, canonical correlation-based methods can be used only
for coregistered data, while nonmultiview methods such as
KPCA and (semisupervised) transfer component analysis
[(SS)TCA] cannot align more than two domains at a time.
In the following, we compare a series of methods on
the challenging problem of transferring a classifier over a
multiangular sequence of images over Rio de Janeiro [52],
illustrated in Figure 6. More details on this example can be
found in [38]. The images are not coregistered but are all
acquired from a single pass of the WorldView2 sensor. For
this reason, the only shifts observed are due to angular effects. The problem is an 11-classes problem, and a separate
ground truth is provided per each image (Table 2).
The adaptation experiment is designed by taking the
nadir image (off-nadir angle i = 6.09 %) as the source image and using all the others as target images. We apply
the PCA, KPCA, graph matching (GM), and semisupervised manifold alignment (SSMA) transforms and then
train a classifier using 100 labeled pixels from the source
domain and predict all of the target domains using that
classifier, without further modifications. For PCA, KPCA,

−38.79°

−29.16°

TABLE 2. ThE NUmBER Of LABELED PIxELS AVAILABLE fOR
EACh DATA SET IN ThE mULTIANgULAR ExPERImENTS
(i = Off-NADIR ANgLE).
i

- 38.79 %

- 29.16 %

6.09 %

26.76 %

39.5 %

Water

83,260

79,937

66,084

63,492

54,769

Grass

8,127

Pools

244

223

195

trees

4,231

4,074

3,066

3,046

concrete

707

719

696

Bare soil

790

811

asphalt

2,949

2,827

Gray
buildings

6,291

6,061

5,936

4,375

4,527

red
buildings

1,147

1,080

1,070

1,046

1,042

White
buildings

1,683

1,571

shadows

1,829

1,056

705

512

525

tarmac

5,179

2,166

2,758

CLASS

and GM, the adaptation is done for each target domain
separately, while, for SSMA, a single adaptation projection is obtained for all domains at once. For SSMA, we
also used 50 labeled pixels per class from each target domain. To be fair in the evaluation, the projections for the
PCA, KPCA, and GM methods are obtained in an unsupervised way, but then the classifier is trained using
the original training points from the nadir acquisition,
stacked to the transformed labeled pixels of the domain
to be tested. We also add a best-case scenario, where we
directly use labeled samples from the target domains for
the classification. The results are illustrated in Figure 7.
The prediction in the off-nadir images using the original training samples from the nadir image leads to poor
results, especially for strong off-nadir angles. All of the
methods considered leverage the decrease in performance
and lead to a quasi-flat prediction surface (meaning that
the model can predict correctly, regardless of the angular configuration) with particularly good performance
by the SSMA method, which seems to best align the data

6.09°

26.76°

39.5°

FiguRe 6. The five images of the Rio de Janeiro angular sequence [52].
june 2016

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Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - June 2016