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USE OF FEATURES DERIVED FROM PROPORTIONS OF CLASSES IN A 
PIXEL FOR THE MULTISPECTRAL CLASSIFICATION OF REMOTE SENSING IMAGES 
Ana Paula D. Aguiar 
Nelson D. A. Mascarenhas 
Yosio E Shimabukuro 
Divisao de Processamento de Imagens - DPI 
Instituto Nacional de Pesquisas Espaciais - INPE 
Caixa Postal 515 - CEP 12201 
Sào José dos Campos, SP - Brazil 
ABSTRACT: 
An analysis of the use of features derived from class proportions in a pixel for the multispectral 
classification of reforested areas in Landsat images is performed. Through a Linear Mixing Model, synthetic 
bands derived from those proportions are obtained either through the Constrained or the Weighted Least 
Squares Procedures. The method indicates that the synthetic bands offer an alternative to the well known 
dimensionality reduction techniques such as Principal Components or Canonical Analysis. Furthermore, those 
bands provide a useful tool for visual interpretation, since they contain information that is related to 
physical concepts (proportions) more easily assimilated than the class spectral signatures. 
KEY WORDS: Mixing Model, Feature Reduction, Least Squares Methods, Classification, Image Analysis, Landsat, 
Thematic. 
1. INTRODUCTION 
In Remote Sensing satellite images, the size of the 
pixel, in general, may include more than one type 
of terrain cover. When these sensors observe the 
earth, the measured radiance is the integration of 
the radiance of all the objects that are contained 
in the pixel, implying the existence of the so- 
called mixture problems. 
Two main approaches have been used in the technical 
literature to solve the mixture problem: 
a. To improve the area estimates obtained by 
conventional classification methods, which are 
mainly based on the spectral characteristics of the 
Pixels. In general, one class corresponds to a 
single type of terrain cover. Therefore, the signal 
obtained by the combination of two or more class 
will not be representative of any of these classes 
and, as a result, an incorrect estimation of the 
area of each class is obtained. Under this 
approach, one may mention the works performed by 
Horwitz et al.(1975) and Ardeo(1983). The main idea 
that guides this approach is to substitute the 
conventional classification methods by the 
estimation of the proportions of classes within a 
pixel in the computation of the total area of each 
class in a scene, 
b. To develop methods that involve synthetic images 
derived from proportions of the objects that are 
contained in the image. The present work is 
included in this approach, as it is described in 
the following paragraphs. 
Detchmendy and Pace (1972) developed a linear 
mixing model to explain the variations found on the 
spectral class signatures. The basic hypothesis of 
such model is that these variations are mainly 
caused by structural target characteristics at the 
sub-pixel scale, These variations can be 
interpreted as a function of the proportions of the 
materials (called primary components) that 
constitute scene, 
As an example, according to Shimabukuro(1987), in 
forested areas, three main components are found: 
tree canopy, soil and shadow. Adams et al.(1990) 
describe the types of land use found in Amazon 
Forest, in terms of four components: vegetation, 
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Soil, shadow and wood. 
Shimabukuro proposes the use of an image derived 
from the shadow component in each pixel of the 
image, called shadow image, as an indication of the 
structure variations on the forest, that is, the 
estimated shadow proportions in an image indicate 
variations in age, type and shape of tree crown 
cover. 
The objective of the present work is to analyze the 
results obtained in the multispectral image 
classification (in particular through the Maximum 
Likelihood criterion under the gaussian hypothesis) 
with the use of synthetic bands derived from the 
proportions of primary components within the 
pixels. Such bands are derived not only from the 
shadow component, but also from other components of 
the scene. 
The adopted Linear Mixing Model, the problem of 
estimating the primary components proportions 
within the pixels and the synthetic bands 
generation are described in Section 2. 
There is a relationship between the number of 
features used in the classification procedure and 
the corresponding computational effort. For the 
Maximum Likelihood classifier, this relationship is 
quadratic. Therefore, it is important to assure the 
use of the minimum number of features for an 
efficient classification (Richards, 1986). 
Some of the feature reduction mainly used in Remote 
Sensing are based on the Jeffries-Matusita  (J-M) 
distance and the Principal Components and Canonical 
Analysis transformations (Section 3). These methods 
are also useful for the visualization of color 
composites of multispectral images (Richards, 
1986). 
The Mixing Model can be regarded as a tool to 
reduce the dimensionality of the feature space to 
the number of mixture components. In the experiment 
presented in this paper (Section 4), the results 
obtained through maximum likelihood classification 
with the use of bands derived from conventional 
feature reduction procedures, and these synthetic 
bands derived from the Mixing Model are compared.