ul 2004
ned by
; in the
where
ata sets
lisation
1emical
bands.
:lecting
IS; (e.g.
tion of
analyte
portant
iffering
rovided
remove
produce
'serving
other
tort the
acity of
«ground
ntitative
features
and the
sed for
oreover,
ectra to
accurate
ver and
- project
ntifying
rspectral
vestigate
stermine
plication
eviously
on with
n set of
jes were
after the
using an
is. In the
rom leaf
leaf area
sed were
reof) at
+ 1999),
bushland
methods
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
2.2 Analytical methods
WA was implemented within Matlab 6.1 using the Wavelet
Toolbox (v.2.1). Multilevel 1-D wavelet decompositions were
performed on reflectance spectra using the range of different
wavelet basis functions available in this package.
Approximation and detail coefficients were extracted for each
spectrum and a stepwise multiple linear regression was
performed on the wavelet coefficients and pigment
concentrations of the leaves and canopies under investigation. A
95% confidence interval was used in the stepwise procedure
and up to 9 terms were permitted in the regression model
(however, in most cases the number of terms selected ranged
between 3 and 6). The predictive capabilities of the regression
model were evaluated by calculating the coefficient of
determination for prediction - the averaged coefficient of
determination with one observation removed from the model
(leave-one-out cross validation).
3. RESULTS
For all leaves and canopies sampled a number of wavelet basis
functions (wavelet families) produced coefficients from which
multiple regression models could be derived that were
correlated with pigment concentrations: Daubechies wavelets
(shortened to 'db' subsequently); Symlets ('sym'); Coiflets
('coif); Biorthogonal wavelets ('bior); and, Reverse
biorthogonal wavelets ('rbio'. Generally the higher order
wavelets within each family produced the highest correlation
with pigments- hence the results for these wavelets are
displayed below.
3.1 Individual leaves and stacks of leaves.
The range of pigment concentrations generated using the
individual leaves and leaf stacks was large: 13 to 3235 mg.m?
for Chl a, 8 to 2168 mg.m™ for Chl ^ and 80 to 1447 mg.m for
Cars. Even over this large range of concentrations the multiple
regression models derived from wavelet decomposition of
reflectance spectra displayed high correlation with pigment
concentrations.
sym8 db8 coif$ bior6.8 rbio6.8
Chla 0.863 0.935 0.925 0.899 0.872
Chlb 0.863 0.863 0.891 0.886 0.847
Cars 0.637 0.743 0.486 0.761 0.715
Chltot 0.863 0.908 0.903 0.892 0.865
Table 1. R^ values for multiple regression models,
deciduous broadleaves.
Table 1. shows the coefficients of determination derived from
multiple regression models based upon spectral decomposition
using five particular wavelets. In all cases the coefficient of
determination for prediction was slightly lower than the values
depicted in the table. Other wavelets within each family
produced lower correlations. As the table, for most wavelets,
there were lower correlations for Cars than for the chlorophylls
= this concurs with previous findings in investigations of other
spectral approaches.
881
3.2 Bracken canopies
Table 2. demonstrates that for bracken canopies the wavelet
decomposition can produce regression models with high
correlations with pigments. Again, correlations are lower for
Cars than Chis.
sym8 db8 coif$ bior6.8 rbio6.8
Chla 0.910 0.915 0.901 0.809 0.782
Chib 0.902 0.873 0.882 0.812 0.798
Cars 0.686 0.732 0.505 0.675 0.701
Chltot 70.905 0.908 0.891 0.810. 0.791
Table 2. R? values for multiple regression models,
bracken canopies.
3.3 Matorral canopies
As table 3 demonstrates, correlations derived for the matorrral
canopies are lower than those for bracken and deciduous
broadleaves.
sym8 db8 coif$ bior6.8 rbio6.8
Chla 0.760 0.785 0.801 0.695 0.608
Chib 0.755 0.764 0.789 0.687 0.599
Cars 0.656 0.710 0.678 0.600 0.502
Chltot 0.758 0.772 0.702 0.692 0.600
Table 3. R? values for multiple regression models, matorral
canopies.
4. CONCLUSIONS.
This initial investigation of wavelet decomposition has revealed
that this technique can produce results that are comparable with,
and in some cases superior to, existing spectral approaches to
pigment quantification from reflectance spectra. This provides
support for further work on the technique, particularly in the
context of testing the robustness and extendibility of the
approach. In the first instance this can be done by combining
the data sets of the various leaf and canopy samples used in the
present study, then by employing additional data sets pertaining
to a wider range of vegetation types. Radiative transfer models
will be of particular value in providing an experimental
platform to investigate issues which are difficult to address
comprehensively in lab or field investigations — notably, the
effects of viewing and illumination geometry and canopy
architecture (i.e. LAD) on the robustness of the wavelet
decomposition techniques, together with the consequences and
emergent properties of many different combinations of
biochemical and biophysical leaf and canopy characteristics,
differing sensor characteristics and atmospheric effects.
Refinements to the wavelet decomposition technique will be
made through the development of automated approaches for the
selection of appropriate wavelet basis functions, application of
