A 4D MORPHOLOGICAL SCALE SPACE REPRESENTATION FOR HYPERSPECTRAL
IMAGERY
Konstantinos Karantzalos
Laboratoire de Mathématiques Appliquées aux Systèmes (MAS)
Ecole Centrale de Paris, Chatenay-Malabry, France
konstantinos.karantzalos@ecp.fr
Commission VII/3
KEY WORDS: Imaging spectrometry, Mathematical morphology, Anisotropic diffusion, Image simplification, Levelings, Denoising
ABSTRACT:
In this paper, a 4D scale space representation is introduced aiming at denoising, smoothing and simplifying effectively airborne and
spaceborne hyperspectral imagery. Our approach is based on a novel morphological levelings’ vectorial formulation, which by integrat
ing spatial and spectral information is able to produce elegantly simplified versions (scale spaces) of the initial hypercube. In addition,
their construction is constrained by vector-valued anisotropic diffused markers which still respect the special hyperspectral data prop
erties. In contrast to earlier efforts, under such a morphological framework the simplified scale space hypercubes are not characterized
by spurious extrema or asymmetrical intensity shifts and their edges/contours are not displaced. Experimental results demonstrate the
potential of our approach, indicating that the proposed representation outperforms earlier ones in quantitative and qualitative evaluation.
1 INTRODUCTION AND STATE-OF-THE-ART
Imaging spectrometry [Goetz et al., 1985] and hyperspectral sen
sors have experienced significant success in recent years. By
offering repetitive, consistent and comprehensive data with en
hanced discrimination capabilities due to their high spectral res
olution, they possess a great potential for geoscience and remote
sensing applications. Environmental monitoring, natural resource
exploration, land-use analysis, terrain categorization, military and
civil government applications for pervious/ impervious surface
mapping have been much eased, while further applications in
medicine, biology, pharmaceuticals, agriculture and archaeology
expand the user community [Landgrebe, 2003,Maathuis and van
Genderen, 2004,Schmidt and Skidmore, 2004, van der Meer, 2006,
Plaza et al., 2008]. Note that for all the above applications the
accuracy of the extracted information, through classification and
other object detection procedures, is of major importance.
It is worth mentioning, however, that the reported average classi
fication accuracy of remote sensing imagery is about 73% [Wilkin
son, 2003] and it has not changed significantly in recent years. In
addition, optimally reducing the dimensionality of hyperspectral
data is still an open problem [Plaza et al., 2008]. Band selection
techniques -which are not, usually, generic and may discard some
bands that contain valuable information- as well as feature extrac
tion methods -which project and may blur, the data into a low
dimensional subspace- are actually a trade-off between making
the problem simpler and losing on classification accuracy [Brun-
zell and Eriksson, 2000, Webb, 2002]. The assumptions on the
possible statistical interpretation/separation of terrain classes do
not, in the general case, hold when these methods are applied di
rectly to the initial degraded and noisy hypercube and not to an
elegantly simplified version of it. Therefore, although the hyper
spectral imaging market is rapidly increasing - soon with new,
lighter, less expensive, higher performing generations of sensors-
there still remain several challenges, regarding their multidimen
sional data processing, that need to be addressed [Plaza et al.,
2008].
First of all, the natural variability of the material spectra, noise,
physical disturbances and degradation added by the transmission
media and the sensor system, reduce the separability of the dif
ferent structures in hyperspectral imagery and diminish the ac
curacy of subsequent segmentation and classification processes.
The increased significance of smaller spatial and spectral varia
tions among pixels implies, also, that smaller amounts of noise
are now likely to have a bigger impact on the results extracted
from this kind of imagery. Even thought any denoising process
has a significant impact on the accuracy of the results, many stud
ies do not use any strict optimizing criteria when selecting the ap
propriate smoothing methods, thus, negatively affecting the out
come of subsequent analysis [Vaiphasa, 2006].
The right balance has to be found, in order to minimize not only
the effect of noise but also the effect of the denoising proce
dure which should, moreover, take into account that objects in
images appear in various scales and thus, information has to be
gathered from various image scales [Lindeberg, 1994, Paragios
et al., 2005]. Towards this end, Anisotropic Diffusion Filtering
(ADF) has been employed for hyperspectral imagery delivering
promising results in improving classification accuracy by reduc
ing the spatial and spectral variability of images, while preserv
ing the boundaries of the objects ( [Lennon et al., 2002, Duarte-
Carvajalino et al., 2007, Martin-Herrero, 2007] and there refer
ences therein). However, such a diffusion (smoothing) scale space
approach, which only recently was fully adapted to the special
spatial/spectral properties of hyperspectral imagery [Martin-Herrero,
2007] may reduce the problems of ad hoc inspections or isotropic
filtering but does not eliminate them completely, since spurious
extrema and intensity shifts may still appear [Meyer and Mara-
gos, 2000, Karantzalos et al., 2007] (Figures 1 and 2). figure
Towards the same direction, other nonlinear scale-space represen
tations, like those based on mathematical morphology, consider
the evolution of curves and surfaces as a function of their geom
etry. Such morphological-based approaches have been, recently,
proposed for processing hyperspectral imagery (e.g. [Benedik-
tsson et al., 2005, Plaza et al., 2005]). However, conventional
multiscale morphological scale-spaces like dilations and erosions
(of increasing structure element size) displace objects boundaries
[Jackway and Deriche, 1996]. Furthermore, the more sophisti
cated openings and closings by reconstruction treat image fore-
