AN INFORMATION THEORIC IMAGE VISUALIZATION SYSTEM 
John S. Powers 
NOAA/NESDIS/Interactive Processing Branch 
Washington, D.C. USA 
ABSTRACT: 
The mathematics of information theory may be used to visualize 
the metrics of information embodied by digital multispectral 
imagery. These visualizations are analogous to the processing 
which occurrs at the retinal level of biological visual systems. 
The utility of the visualizations lies in their ability to reveal 
subtle nuances of phenomena in satellite remote sensor imagery, 
and in their shared mathematical foundations with theoretical 
studies of systems, complexity and diversity. 
KEY WORDS: entropy, image processing, information theory 
Introduction 
The traditional model of digital imagery 
is that of a record of spatially unique, 
instantaneous physical measurements within 
selected intervals of the electromagnetic 
spectrum. From the perspective of 
conveyed information at a point, all 
points on the image are regarded as 
equivalent. Variations on this model 
include measurements of deviations from a 
datum, such as terrain elevation or 
atmospheric pressure. 
At a different level of abstraction, an 
image may be regarded as an integrated set 
of pure information, mathematically 
defined. In the integrated model, each 
instantaneous value on an image is a 
function of all other instantaneous values 
over the entire image field. The 
abstraction of an absolute physical 
measurement at a point is superseded by 
the abstraction of information conveyed at 
a point relative to an organized system. 
This is the model which best describes the 
retinal stage of biological imaging 
systems. 
A robust mathematical definition of 
information was first articulated by 
Claude Shannon, extending and adapting the 
mathematics of classical thermodynamics 
(Shannon, 1949). The theory was 
originally conceived to solve the problem 
of optimizing electronic communications in 
the presence of noise over limited carrier 
bandwidths, but has since been accepted as 
a rigorous mathematical foundation for 
broadly applicable metrics of system 
organization and diversity. 
Organization and diversity are fundamental 
characteristics of natural systems, 
possessing strong associations with system 
behavior, resiliance and adaptability to 
change. Information theory has fascinated 
researchers with its potential as a 
paradigm integrating within a single 
conceptual and mathematical framework the 
diverse fields and scales of inquiry into 
systems. The theory has also been 
criticized as being frequently 
overextended or misapplied to areas where 
the mathematical justifications for its 
use are tenuous, and the interpretations 
of its results questionable. These 
682 
criticisms are well founded, and rigorous 
mathematical prerequisites for the 
application of the theory must be met. 
Discrete Markoff Processes and Ergodic 
Sources 
A fundamental concept of information 
theory is that of a discrete Markoff 
process. The general case of a discrete 
Markoff process is that of a system with a 
finite number of discrete states S1, 
S2...Sn. For each state of the system 
there must exist a set of transition 
probabilities Pi(j) which describe the 
probability that a system in state Si will 
transition to state Sj. A discrete 
Markoff process becomes an information 
source by producing a measurement at each 
transition from one state to another. 
Among possible Markoff processes, 
information theory concerns a distinct 
class known as "ergodic" processes. An 
ergodic Markoff process is a process which 
generates sequences of values which share 
the same statistical properties. As the 
length of a sequence from an ergodic 
Markoff process increases, the sequence 
statistics will cluster around limits 
characteristic of that ergodic Markoff 
process. Such clustering will exist even 
though every sequence may be unique and it 
may be impossible to predict the next 
state of any sequence from preceding 
states. Shannon equates the ergodic 
property with "statistical homogeneity." 
All human languages are examples of 
discrete ergodic Markoff processes. The 
phenomenon of "texture" may likewise be 
considered an expression of discrete 
ergodic Markoff processes in the spatial 
domain. Finally, the superposition of 
ergodic Markoff processes is itself an 
ergodic Markoff process (Moles, 1967), as 
is the case with music. 
It is a necessary assertion that a 
multispectral imaging scanner viewing the 
earth meets the definition of a discrete 
Markoff process, and that a digital 
multispectral image may be regarded as 
record of a discrete Markoff process. 
This assertion follows from the 
observation that transitions of 
instantaneous physical measurements from 
one state to another in space may be 
described by a finite set of transition 
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