CONSIDERATION OF THE UNCERTAINTY IN UNCERTAIN KNOWLEDGE 
FOR KNOWLEDGE BASED IMAGE CLASSIFICATION 
Shabai Huang Claude R. Dugauy 
Ph.D. Candidate Professor 
Laboratory for Earth Observation & Information Systems 
Department of Geography 
University of Ottawa 
Ottawa, Canada K1N 6N5 
Aining Zhang 
Research Engineer 
Applied Research & Technology Service 
Geographical Services Division 
Canada Center for Mapping 
Ottawa, Canada K1A 0E9 
ISPRS Commission III 
ABSTRACT 
A key issue in knowledge based remotely sensed image classification is the approach to deal with the uncertainty 
existing in inexact knowledge. The uncertainty problem can be differentiated into two types: one is the uncertainty 
directly associated with uncertain knowledge; the other refers to the uncertainty existing in the certainty values of 
inexact knowledge. Expert system research has provided numerous theories for dealing with the former type of 
uncertainty, while few endeavors are found to address the latter type. This paper is devoted to the second type of 
uncertainty, namely, the Uncertainty In Uncertainty (UIU) problem. Based on an analysis of the importance of this 
issue, the paper presents a mathematical model for dealing with the uncertainty in uncertainty values, and 
discusses the methods to estimate various variables and parameters involved in the model. A case study is 
presented which has preliminarily proven the effectivity of the uncertainty model. 
Key Words: Uncertainty reasoning, Uncertainty in uncertainty, Knowledge-based system, Expert system, Image 
classification, Mathematical modeling, Remote sensing. 
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INTRODUCTION 
The incorporation of ancillary data into the 
classification of remotely sensed images has proven to 
be effective in improving classification accuracy 
(Middelkoop and Janssen, 1991; Skidmore, 1989; Kenk 
et al. 1988; Wu et al, 1988). Ancillary data, such as 
topographic information, soil maps and temporal 
relationships, can be applied effectively only if they 
have known relationships to the classes in the images. 
This implies that the utilization of ancillary 
information in image classification requires the 
incorporation of declarative knowledge that indicates 
such relationships into spectrally-based classification. 
Thus, the knowledge based system approach has been 
widely applied to multi-source image classification. 
Meanwhile, knowledge on the relationships between 
ancillary data and image classes is usually acquired 
from relevant specialists or based on statistics, 
therefore, the declarative knowledge inevitably 
encapsulates uncertainty or ambiguity. This makes the 
methodology for uncertainty reasoning an important 
issue in multi-source remote sensing image 
classification. 
Research in the expert system domain has provided a 
variety of methods for dealing with the uncertainty 
problem. Among them are probability theory, 
uncertainty theory, the Dempster/Schafer theory, 
possibility theory, plausibility theory, etc. (Frost, 1986; 
Payne and McArthur, 1990). These theories, though 
differing from each other, all deal with the 
representation of inexact (or uncertain) knowledge and 
reasoning based on inexact knowledge. However, 
beneath the uncertainty values of inexact knowledge, 
there actually exists another type of uncertainty, 
namely, the reliability of the uncertainty values. For 
example, a certainty factor associated with a rule stated 
by an expert may have uncertainty related to the 
sufficiency and representativity of the sample used by 
the expert to derive this rule; the probability of certain 
diseases' occurrence given certain symptom has its 
inherent uncertainty related to the data accuracy and 
sufficiency in the database where the probability is 
derived. This type of uncertainty is not handled in all 
those theories dealing with uncertainty. 
This paper addresses the uncertainty in uncertainty 
(UIU) problem of inexact knowledge. The necessity of 
addressing this topic is discussed through the analysis 
of the sources that cause the UIU problem, and the 
inadequacy of uncertainty reasoning methods 
commonly used in knowledge-based systems to the 
UIU problem. An approach for dealing with this 
problem is then given. It includes the definition of the 
UIU concept, the establishment of a mathematical 
model for dealing with the uncertainty, and the 
estimation of variables and parameters involved in 
the model. Based on the uncertainty model, a case 
study is presented in order to demonstrate the 
utilization and effectivity of this model. A 
preliminary conclusion is drawn based on the 
experiment that, by taking the UIU problem into 
account, the classification accuracy can be improved. 
NECESSITY OF CONSIDERING THE UNCERTAINTY 
IN UNCERTAINTY VALUES 
Sensing Image 
The Uncertainty in Remote 
Much of the knowledge with which humans reason is