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ROBUST MIXED PIXEL CLASSIFICATION IN REMOTE SENSING
P Bosdogianni, M Petrou and J Kittler
University of Surrey, Dept. of Electronic and Electrical Engineering,
Guildford GU2 5XH, United Kingdom
E-mails: {p.bosdogianni, m.petrou, j.kittler}@ee.surrey.ac.uk
Commision VII, Working Group 6
KEY WORDS: hough, unmixing, classification, multispectral, satellite, Landsat, simulation
ABSTRACT
In this paper we present a novel method for mixed pixel classification where the classification of groups of mixed pixels is
achieved by using robust statistics. The method is demonstrated using simulated data and is also applied to real Landsat TM
data for which ground data are available.
1 INTRODUCTION
The problem of mixed pixel classification is a major issue
in Remote Sensing and Geography and many approaches
have been developed to deal with it [Adams et al., 1986,
Foody et al., 1993, Lennington et al., 1984, Li et al., 1985,
Marsh et al., 1980, Settle et al, 1993, Smith et al.,1990]. In
the past we addressed the problem of mixed pixel classifica-
tion when whole regions of mixed pixels have to be classified
by treating the distribution of pixels in each region as a ran-
dom distribution [Bosdogianni et al., 1994]. In this work we
address the same problem but in a way that is applicable to
cases that our previous approach is unreliable, namely when
outliers are present.
The motivation of our work is to monitor burned forests for a
few years after the fire so that the regeneration processes can
be evaluated. In particular, we are interested in assessing the
danger of desertification conditions ensuing in the site of a
burned forest in the Mediterranean region. If the forest does
not show signs of recovery a couple of years after the fire, it
probably has to be artificially re-forested to prevent further
erosion. Quite often, different types of vegetation grow in
a burned region. It is usually the case that this new vege-
tation presents a deterioration of the quality of the flora of
the region. The main type of forests that are common in the
Mediterranean region consist of aleppo pine (pinus halepen-
sis). Thus, for the purpose of our work, we are interested in
assessing the degree of presence of three classes in a region:
aleppo pine, bare soil and other vegetation, using Landsat
TM images.
There is a major problem, however, when one deals with real
data: The data tend to be very noisy and inaccurate. The
statistics computed from them tend to be distorted and it
is difficult to obtain consistent results. Thus, a more robust
way of solving the problem is needed.
2 THE PROPOSED METHOD
In the linear mixing model adopted here, it is assumed that
the pixel value in any spectral band is given by the linear
combination of the spectral responses of each component
within the pixel, so the model can be expressed as:
w=az+by+cz (1)
where w is the known spectral reflectance of a mixed pixel,
t, y and z are the known spectral reflectances of the three
85
possible cover components within the mixed pixel and a, b
and c are the proportions for each component contained in
the mixed pixel that have to be estimated.
If we consider again the linear mixing equation mentioned
above, we see that it actually is the equation of a hyper-plane
in luminance space where we measure one type of luminance
along each axis. What we are interested in identifying are
the parameters a, b and c for this plane. The method usually
used for this purpose is that of least squares fitting. It is
well known, however, that the method of least squares is
particularly sensitive to outliers. What we propose in this
paper is the use of Hough transform to identify the best values
of a, b and c. Hough transform is known to be a robust
technique which can tolerate large amounts of outliers and
still produce good results. In its most commonly used form it
is used to identify straight lines in images, but more generally
Hough transform can be thought of as a transformation into
the parametric domain where we seek to identify sets of real
data that indicate the same values of the parameters for the
parametric hyper-surface they define.
In our case this hyper-surface is a plane defined in the 3D do-
main (z, y, z), which is parameterised by different values of
w. Thus, our method consists of the definition of an accumu-
lator 3D array defined in the parametric (a,b, c) domain. For
each quadrupole (x, y, z, w) we have a different plane defined
in the (a,b,c) domain. The surface of this plane intersects
various cells of the accumulator array the occupancy number
of which is incremented by 1. When all possible quadruples
of the data have been considered, the highest peak in the
accumulator array defines the best values of the mixing pa-
rameters a, b and c. In reality, of course the problem is even
simpler than that, because we know that the values of these
parameters have to sum up to 1, so we can eliminate the
third one in terms of the other two and the linear model of
equation (1) now looks like:
w— z-(r-z)a-d(y-— z)b (2)
Then our accumulator array is only 2D and it can be sampled
with sufficiently high accuracy. The next step in our optimi-
sation procedure is to estimate the bin size in the accumulator
space for the two parameters a and b. In our applications we
do not really need to know the values of a and b to better
than two significant figures accuracy, so the size of our accu-
mulator array will not be larger than 100 x 100, but generally
it will be a lot smaller.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B7. Vienna 1996
