The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
Figure 5: Smoothing and simplifying hyperspectral imagery 
(©Norsk Elektro Optikk). First column: A 3D view of the ini 
tial hypercube (top) and a zoom on the band number #94 (mid 
dle). Second and third column: the resulting hypercubes and the 
corresponding bands after applying the ADF (second column) 
and the proposed AML (third column). Contrary to ADF, which 
smoothed without preserving image flat zones, AML simplified 
and stayed constantly close to the initial hypercube intensity val 
ues and structure. 
adaptive time step At = Almax/raacc(|trace(TH)|) or on an 
other selected one. In cases where just a single simplified hy 
percube is needed, the coefficients can be customized accord 
ingly. The proposed, thus, vectorial leveling AML takes its final 
form when in Equation (4) the family of markers h n are derived 
from the anisotropic diffused markers X n of Equation (8). Such 
anisotropic markers, which do respect hyperspectral data speci 
ficities, can naturally ameliorate the simplification process, with 
out, in addition, demanding a search for selecting the appropriate 
structure element size and type, as the classical morphological 
operators do. 
4 EXPERIMENTAL RESULTS - EVALUATION 
The developed vectorial Anisotropic Morphological Leveling AML 
was applied to a number of hyperspectral images and its evalua 
tion was carried out by both a qualitative and a quantitative as 
sessment. Datasets from the HySpex VNIR-1600 airborne sensor 
(©Norsk Elektro Optikk A/S) with 160 channels (400-1000nm), 
from the CASI-1500 airborne sensor (©ITRES) with 36 chan 
nels (380-1050nm) and from EOS-1 Hyperion (©USGS) space- 
borne sensor with 220 channels were available. Throughout the 
evaluation procedure the compared ADF was the same with the 
one that was used for the construction of the AML and each scale 
n was derived after three iterations t. Both were also compared 
with the classical ML after a standard channel by channel process 
to the resulting ADF hypercube. For the quantitative evaluation 
apart from the standard RMSE and NMSE measures -which give 
a quantitative sense for the extent of variation between the inten 
sity values of the compared images- the recently proposed com 
plementary quality measure of SSIM [Wang et al., 2004] was, 
also, employed because it is able to compare effectively local 
patterns of pixel intensities under a perceived visual quality. The 
lower RMSE and NMSE and the bigger SSIM values designate 
the better filtering result. 
Table 1 : Quantitative Evaluation 
Test Data 
Type of 
Quantitative Measures 
Filter 
RMSE || NMSE | 
SSIM 
Figure 1 
ADF 
0.012 
0.009 
0.996 
ML 
0.009 
0.004 
0.998 
Hypercube 
AML 
0.006 
0.002 
0.999 
Figure 1 
ADF 
0.097 
0.156 
0.985 
ML 
0.035 
0.020 
0.996 
Band #33 
AML 
0.034 
0.018 
0.998 
Figure 1 
ADF 
0.068 
0.021 
0.944 
ML 
0.055 
0.013 
0.974 
Band #87 
AML 
0.049 
0.011 
0.974 
Figure 2 
ADF 
0.147 
0.093 
0.982 
ML 
0.049 
0.010 
0.997 
Band #100 
AML 
0.041 
0.007 
0.998 
Figure 5 
ADF 
0.009 
0.004 
0.998 
ML 
0.004 
0.001 
0.999 
Hypercube 
AML 
0.003 
0.001 
1.000 
Figure 5 
ADF 
0.052 
0.018 
0.973 
ML 
0.025 
0.005 
0.992 
Band #94 
AML 
0.020 
0.003 
0.995 
Noisy 
ADF 
0.013 
0.012 
0.996 
ML 
0.009 
0.007 
0.997 
Hypercube 
AML 
0.008 
0.004 
0.998 
In Figure 1, 3D views of the initial hypercube and the resulting 
ones from the ADF and the AML are presented, together with 
two corresponding bands #33 and #87 (filtering scale n=3). 
The ADF smoothed strongly the data and created some intensity 
shifts. In contrast the AML simplified the data but kept a closer 
relation with the initial hypercube intensity values. This can be 
more clearly verified by a close look at Figures 3 and 4, where 
cross sections along the spatial y-axis and the spectral axis are 
presented, respectively. One can observe that even thought all the 
compared filters did not displace edges, the AML almost every 
where stayed closer to the initial hypercube. AML simplified the 
image in the spatial directions by enlarging or creating new flat 
zones (levelled regions with constant intensity values), retaining 
all its 2D scale space properties. In the spectral direction it ac 
counted for large intensity variations (spike-like features) and at 
the same time stayed close to the initial hypercube values. The 
above observations can be further confirmed by the performed 
quantitative evaluation (Table 1). In all cases (Figure 1), the AML 
resulted to the lower RMSE and NMSE values and to the larger 
structural similarity with the original image (SSIM). 
In Figure 2, the initial and three of the resulting AML scale space 
images are presented (scales n=2, 3 and 4). The increasingly 
simplified versions of the original spatial image structure can be 
observed. The quantitative comparison between AML’s result (at 
scale n=4) with the corresponding ML and ADF (Table 1), indi 
cate that the AML scored better in all measures. Furthermore and 
evaluating the compared filtering techniques in another dataset 
(shown in Figure 5), approximately the same conclusions were 
derived. In Figure 5, 3D views of the initial hypercube and the 
ones resulting from the ADF and the AML are shown, together 
with the corresponding band #94. By comparing qualitatively, 
all filtering results in the same scale (n=6), it can be observed 
that the difference between diffusing (smoothing with ADF) and 
simplifying (AML) adjacent intensity variations, is that a more el 
egantly enhanced version of the original image is obtained from 
the AML. Both methods respect image edges but the proposed 
AML enforces the creation of flat regions instead of diffusing 
inside them. This process obliges, also, AML to follow more 
constantly the original hypercube’s intensity. The above obser 
vations can be confirmed by the quantitative measures in Table 
1 which indicate that the AML scored better in all measures, 
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