Fig. 1 - GEOCLASS Image Segmentation Process
THE PROBLEM OF MIXTURE
THE LINEAR MIXTURE MODEL VERSUS THE FUZZY MOTEL
Vitor Haertel
Associate Professor
Jorge Silva Centeno, Néstor A.Campana
Students
Federal University of Rio Grande do Sul,UFRGS,Brazil.
ABSTRACT
In natural scenes it often happens that more than one class is present in a pixel.
The pixel spectral response in this case is not representative of either one of the
component classes. One approach to solve this problem is the linear mixture model.
More recently another model, implementing fuzzy mathematical concepts was introduced.
Software compatible with the Brazilian SITIM-
in order to implement and compare both models
150 image processing system was developed
A test area located in the Emas
National Park in Brazil is used in order to identify mixtures involving distinct
proportions of vegetation.
KEY WORDS: Remote Sensing Application, Image Classification, Class Mixture.
1. INTRODUCTION
1.1 The Problem of Mixture
Current methods for image classification
in Remote Sensing are applied on a pixel
by pixel basis, implementing either
probabilistic or deterministic algorithms
(Tou & Gonzalez, 1974, Richards, 1986).
Following these methods, image pixels are
assigned to one of the existing information
classes. Classification is based upon the
radiance recorded by the satellite which
is an integrated sum of the spectral responses
of the materials within the instantaneous
field of view (IFOV) of the sensor (Shima-
bukuro, 1987). In natural scenes, it often
happens that pixels are constituted by more
than one class, i.e.: are mixture pixels.
In this case, the spectral response is not
representative of any individual class,
leading to incorrect classification results.
Mixture pixels occur even in areas covered
by homogeneous vegetation (eg.:agricultural
fields).
Variations in canapy density across the
area may cause varying degree of soil
vegetation mixtures (Haertel, 1991) which,
in turn, will cause variations in image
spectral characteristics.
The current classification methods which
assume that a pixel either belongs entirely
to a class or does not belong to this class
at all, are clearly not capable cf dealing
with the mixture problems. The only way
possible would be to increase the number
of information classes, to account for the
mixture classes. This approach, however,
would require an accurate knowledge of the
mixture classes in the scene, which, in
many cases, is not available and also lead
to higher analysis costs.
The best way of dealing with the mixture
problem in image classification consists in
developing mathematical models capable of
dealing with different proportions of
informations classes in a single pixel.
1.2 Mathematical Models for the Mixture
Problems
Two basic approaches were proposed to deal
with the mixture problem: the LinearMixture
model and the Fuzzy Classification model.
The Linear Mixture model approach has been
reported by several authors. A rather
extensive review of this model is presented
in Shimabukuro (1987) and is reviewed in
section 2. The spectral contribution of each
component class within a pixel is modelled in
a linear relationship. ‚The linear model, as
applied to digital image classification,can
be implemented in two different approaches.
Given the component information: classes
("pure" classes) one can estimate, for every
pixel, its composition in terms of the
component classes (Ranson,1975,Heimes,1977,
Shimabukuro, 1987). A second approach consists
in making use of the Linear Mixture model
to estimate the mean vector and the’ covariance
matrix of the "mixture classes" from the
corresponding parameters associated with
the component classes. This approach allows
the user to "create" the mixture classes
relevant to a particular situation,and is
useful whenever the analyst is interested
in some specific mixtures (eg.: vegetation
and soil due to variations in vegetation
density cover).
Image classification methods like the Gaus-
sian Maximum Likelihood may then be applied
to the entire scene.
907
