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Proceedings of the Symposium on Global and Environmental Monitoring

E.J. Van Kootwijk* and H. van dcr Voet**
* Research Institute for Nature Management, P.O. box 9201, 6800 I IB Arnhem, The Netherlands
** Agricultural Mathematics Group, P.O. Box 100, 6700 AC Wagcningen, The Netherlands
Presented at ISPRS Commission VII Symposium, September 17-21, 1990, Victioria, B.C. Canada
Abstract. Using multivariate regression techniques to establish a relation between pixel values and
percentages ground cover, it was possible to estimate the relative cover per pixel of heather and
grass species. By using an optimization procedure for localising field data in tne image, the quality
of training sets was improved.
Key Words: Regression model, image calibration, training set optimization, heathland.
Air pollution causes a higher atmospheric
input of nutrients in Dutch hcathlands. As a
result, the rate of change from heather to
grass species increases (Berdowski 1987, Hcil
19841. Mapping the changing amounts of
heatner and grass in relation to nutrient input
serves both nature management and environ
mental decision making. This study was carried
out as part of the Dutch National Research
Program on Acidification. The objective was to
develop within one year a mapping method
that would yield quantitative information on a
national scale. Moreover, it had to be suitable
for further development into a monitoring
system. Landsat TM imagery was found to be
the optimal choice as to availability, spatial
resolution, area covered and monitoring poten
Processing satellite imagery of natural veget
ation using classifying algorithms poses serious
difficulties. In fact, interpreting such images is
not a classification problem. Natural vegetation
often exhibits a large spatial and temporal
variability in species abundances, structure and
lifeform. This variability is not to be seen as
noise, but as an important property of the
vegetation. Even heathland, thougn rather
simple in composition, can not be described
rightly in terms of 30 x 30 m squares (the
resolution element of Landsat TM) containing
either heather or grass. The alternation of
grass (mostly Molinia cacrulca and Dcschamp-
sia flexuosa) and heather species (Calluna
vulgaris and Erica tetralix), sometimes in pat
ches, sometimes truly intermingled, is an ecolo
gical factor, related to the physiological and
ecological processes occurring in the vegeta
tion. Most TM pixels contain both heather and
grass, as spatial variation is high relative to
the size of the resolution element. Instead of
classifying pixels, one would like to know the
amount of various cover types that contributed
to individual pixel values. In the absence of an
appropriate canopy reflectance model and an
atmospheric model, regression techniques can
be used to model the relation between cover
and reflectance.
A multivariate calibration model is needed in
order to predict ground cover composition
from reflection data. Denote for pixel i the
ground cover data by the vector x, =
(x, 1 ,...,x IK )’, where K is the number of cover
classes, and the pixel values by the vector y,
= (yi 1 ,...,y iq )’, where q is the number of spec
tral bands. There are two special characteris
tics in this situation. Firstly, the ground cover
data x, are vectors of non-negative values
summing to 1. Secondly, physical theory tells
us to expect that y,j is a linear combination of
the cover fractions x, k (at least under idealised
circumstances). That is:
E(yij) = «Li (1)
where |x kj is the expected pixel value of a pixel
consisting of 100% class k cover in spectral
band j.
To some extent these characteristics lead to
conflicting requirements for the calibration
model, because a linear model will inevitably
be able to predict cover fractions smaller than
0 or larger than 1, whereas any nonlinear
model violates the expected relation (1). In
this paper a nonlinear model is used.
A further point deserving attention is the
possibility of using prior information on
ground cover composition in the population of
ixcls to be predicted. Such information may
e available from external sources or from the
training data. The latter possibility is relevant
especially when the training pixels have been
obtained by a suitable sampling scheme (e.g.
simple or stratified random sampling, or some
form of cluster sampling). However, also in
other situations the assumption is often accep
ted that the training sample is representative
of the whole population. In this paper the
utility of incorporating such prior information
is evaluated.
The problem of predicting cover composi
tion has been considered by several other
authors, c.g. Marsh c.a. (1980), Switzer (1980),
Pech c.a. (1986), Wood and Foody (1989). In