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june 2016 ieee Geoscience and remote sensin G ma Gazine 49 |
acquisitions, in which the spectra are spatially detrended |
using Gaussian processes to avoid shifts related to local - |
ized class variability. In [ 49], the authors perform anom - |
aly 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 map - |
ping 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 exam - |
ple, 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 ef - |
fects. 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 |
.)609 i=% as the source im - |
age and using all the others as target images. We apply |
the PCA, KPCA, graph matching (GM), and semisuper - |
vised 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, and GM, the adaptation is done for each target domain separately, while, for SSMA, a single adaptation projec - |
tion is obtained for all domains at once. For SSMA, we |
also used 50 labeled pixels per class from each target do - |
main. To be fair in the evaluation, the projections for the |
PCA, KPCA, and GM methods are obtained in an un - |
supervised 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 origi - |
nal 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 angu - |
lar configuration) with particularly good performance by the SSMA method, which seems to best align the data TABLE 2. Th E NUmBER Of LABELED PIxELS AVAILABLE fOR |
EACh DATA SET IN Th E mULTIANgULAR ExPERI mENTS |
(i = Off-NADIR ANgLE). |
CLASS i38.79-%29.16-%6.09%26.76%39.5% |
Water 83,260 79,937 66,084 63,492 54,769 |
Grass 8,127 8,127 8,127 8,127 8,127 |
Pools 244 244 223 195 195 |
trees 4,231 4,074 3,066 3,046 3,046 |
concrete 707 719 719 719 696 |
Bare soil 790 790 790 790 811 |
asphalt 2,949 2,949 2,949 2,827 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 1,683 1,571 1,571 1,571 |
shadows 1,829 1,056 705 512 525 |
tarmac 5,179 5,179 5,179 2,166 2,758 |
−38.79° −29.16° 6.09° 26.76° 39.5° |
Figu Re 6. The five images of the Rio de Janeiro angular sequence [52]. |
Authorized licensed use limited to: ASU Library. Downloaded on March 08,2024 at 03:13:37 UTC from IEEE Xplore. Restrictions apply. |
ieee Geoscience and remote sensin G ma Gazine june 201650 |
distributions. This is not surprising, since, among the test - |
ed methods, SSMA is the only one with a clear discrimina - |
tive component that uses labels in all domains to define |
the projections. |
ADAPTING CLASSIFIERS WITH |
SEMISUPERVISED APPROACHES |
A widely used approach to DA is based on adaptation of |
the model of the classifier derived on the source domain |
to the target domain. In the literature, the approach is de - |
fined as semisupervised if this adaptation is based only on |
unlabeled samples of the target domain (no target train - |
ing samples are used). The rationale of semisupervised ad - |
aptation is to use the relations between the distributions of the source and target domains to infer a reliable solu - |
tion to the problem described in the target domain. The |
common assumption of most of the methods is that the |
source and target domains share the same set of classes |
and features. |
The first attempts to address semisupervised DA in re - |
mote sensing image classification were presented in [ 53], |
where a DA technique is proposed that updates the parame - |
ters of an already trained parametric maximum-likelihood |
(ML) classifier on the basis of the distribution of a new im - |
age for which no labeled samples are available. In [ 54], the |
ML-based DA technique is extended to the framework of the Bayesian rule for cascade classification (i.e., the classifi - |
cation process is performed by jointly considering informa - |
tion contained in the source and the target domains). The basic idea in both methods is modeling the observed spaces |
by a mixture of distributions, whose components can be es - |
timated by the use of unlabeled target data. This is achieved by using the expectation maximization (EM) algorithm with the finite Gaussian mixture model. In [ 55] and [56 ], |
DA approaches based on multiple-classifier and multiple-cascade–classifier architectures were defined. Gaussian ML classifiers, radial basis function neural networks, and |
hybrid cascade classifiers are used as base classifiers. The |
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