International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
measurement metric from background pixels, where the background pixels dataset is usually
contaminated since it is usually composed of all the pixels in the image [7]. Robust Mahanlobis
distance based methods construct an iterative procedure [4]. In each iteration the first and second
order statistics are computed to figure out the anomalous distance, then the pixels presenting
distance larger than a predefined threshold would be excluded and the statistics are updated by the
rest dataset. The iteration is done until the rest dataset wouldn’t change. The underlying idea is
that the contamination by anomalies can be gradually eliminated by a dataset shrinking procedure,
and the anomalies can be detected at the same time.
Hyperspectral images contain a large number of spectral bands. Though state-of-art methods
prove promising in separating anomalies from backgrounds, the nonlinear correlations between
different spectral bands are not considered. Different materials present spectrally absorption at
different spectral position, so that the nonlinear correlations are not evitable. Kernel based
anomaly detection methods have made great success, the typical ones are kernel-RX. Another
factor that needs further investigation is that the mixed manner of each pixel is much more
complex than linear mixture model. As the spatial resolution is limited, intimate mixture, instead
of linear mixture, is more widespread and reasonable [8]. In intimate mixtures, the photons are
interacting with all the materials simultaneously. In linear mixtures, the assumption was the
photons scattered off one material at a time. Since intimate mixtures have multiple different
materials in close relation to one another, the photons can bounce from one particle to another
causing different absorption and reflection effects. The result is mixing that cannot be well
captured by simple linear models [8]. Inspired by kernel-RX and robust anomaly detection
methods, we proposed the new robust one, with the detailed steps are presented as following:
Step 1: Since the gram matrix is usually NxN with N being the number of background pixels, it
is not possible to consider all the pixels at one time otherwise it would exceed the computing
capacity very easily. So a k-means clustering method is employed to segment the dataset into k
classes.
Step 2: For each clustered class, all the pixels are projected into the high feature space
x > ¢(x) , constituting a new dataset D. It is assumed that
Step 3: The statistics of these projected pixels from D are figured out, including mean m
and covariance C.
