  The use of distances based on optimal transportation has recently shown
promise for discrimination of power spectra. In particular, spectral estimation
methods based on l1 regularization as well as covariance based methods can be
shown to be robust with respect to such distances. These transportation
distances provide a geometric framework where geodesics corresponds to smooth
transition of spectral mass, and have been useful for tracking. In this paper,
we investigate the use of these distances for automatic target recognition. We
study the use of the Monge-Kantorovich distance compared to the standard l2
distance for classifying civilian vehicles based on SAR images. We use a
version of the Monge-Kantorovich distance that applies also for the case where
the spectra may have different total mass, and we formulate the optimization
problem as a minimum flow problem that can be computed using efficient
algorithms.
