  Remote sensing image classification exploiting multiple sensors is a very
challenging problem: data from different modalities are affected by spectral
distortions and mis-alignments of all kinds, and this hampers re-using models
built for one image to be used successfully in other scenes. In order to adapt
and transfer models across image acquisitions, one must be able to cope with
datasets that are not co-registered, acquired under different illumination and
atmospheric conditions, by different sensors, and with scarce ground
references. Traditionally, methods based on histogram matching have been used.
However, they fail when densities have very different shapes or when there is
no corresponding band to be matched between the images. An alternative builds
upon \emph{manifold alignment}. Manifold alignment performs a multidimensional
relative normalization of the data prior to product generation that can cope
with data of different dimensionality (e.g. different number of bands) and
possibly unpaired examples. Aligning data distributions is an appealing
strategy, since it allows to provide data spaces that are more similar to each
other, regardless of the subsequent use of the transformed data. In this paper,
we study a methodology that aligns data from different domains in a nonlinear
way through {\em kernelization}. We introduce the Kernel Manifold Alignment
(KEMA) method, which provides a flexible and discriminative projection map,
exploits only a few labeled samples (or semantic ties) in each domain, and
reduces to solving a generalized eigenvalue problem. We successfully test KEMA
in multi-temporal and multi-source very high resolution classification tasks,
as well as on the task of making a model invariant to shadowing for
hyperspectral imaging.
