Bethel, James 
  
complex surface such as that of the Earth. However, such data also present some significant subtleties that must be well 
understood and properly dealt with if the full information-bearing potential of such data is to be realized. 
Any given material on the Earth's surface that one may wish to map will exist in a number of states. This leads to a 
given material being characterized by not a single spectral response but by a family or ensemble of spectral responses. 
Quite in addition to a typical or average response, the more general ensemble properties will have characteristics useful 
for purposes of discriminating between materials in that scene. For example, pixels measured of an agricultural crop on 
a given day vary somewhat and this variation will be significantly diagnostic of that crop. Even though the leaves of the 
crop may have spectral characteristics very similar to those of a tree species, a pixel that includes a number of crop 
plants will carry with it characteristics unique to the crop and different from those of a wooded area, because of the 
difference in physical structure of the two types of plants. 
Thus, the process of mapping themes of the Earth's surface is one of labeling pixels whose ensemble have variations 
that are characteristic of the themes of interest. One is not looking simply for the similarity of a pixel to some spectral 
standard so much as looking at the similarity or difference of mixtures of pixel responses. 
The most effective way to represent data for this purpose is in terms of a feature space. The concept is to represent the 
data values of each pixel as components of a vector. Thus a pixel of 200 band data would be a point in a 200 
dimensional vector space, and an ensemble of pixels that represent a given class of surface cover would be a 
distribution in this 200 dimensional vector space. 
The power of hyperspectral data can then be simply illustrated by noting that if one has data measured in 200 bands 
each with 10 bit precision (2? — 1024 shades of gray), then there are 2'° raised to the 200% power individual locations in 
that feature space for a pixel to be found. That number, 2%°%° ~ 10 °° js so large that even if one has a data set of a 
million pixels, the probability of any two pixels occurring in the same location in this space is vanishingly small. Thus, 
since there is no overlap, theoretically, anything is separable from anything else. The difficulty, on the other hand, is 
that one must locate decision boundaries between desired classes in such a large space very precisely in order to achieve 
successful discrimination between all the classes existing in such a data set. That is the task that the analyst faces. 
Much has been learned in the last few years about how to accomplish this analysis. ' An important example of this stems 
from the fact that, because of the large volume of hyperspectral feature spaces, most of the volume available for a given 
data set will be empty, and the significant structure for a specific problem at hand will reside in a lower dimensional 
subspace. Thus it is useful to define an optimal linear transformation on the specific data classes desired to find the 
lower dimensional space most useful for discriminating the data into desired classes. Such transformations are known as 
feature extraction algorithms. 
A group of algorithms for accomplishing the this and other necessary processes have been assembled and made 
available to the public in a program for personal computers called MultiSpec.? Though there are a number of details and 
variations, the basic analysis process is one of 
l. Defining the classes of interest to the analyst by labeling an adequate number of examples of each in the 
data set itself. 
2. Exercising a feature extraction algorithm that basically defines an optimal subspace for this particular 
classification. 
3. Choosing and executing an appropriate classification algorithm in the chosen subspace. 
The process has become simple enough that a sizable hyperspectral data set of perhaps 150 megabytes can be analyzed 
to create a thematic map for 6 to 10 user themes in less than half an hour using less than 3 minutes of computation time 
on a contemporary $3000 personal computer. 
Figure 3 shows an image sequence of such an analysis of a HYDICE data set of the Washington, DC mall area. The 
data set contains 1208 scan lines of 307 pixels ("370,000 pixels) in 210 bands. The primary task of the analyst is to 
specify what classes of surface cover one wishes to discriminate between. In this case, the desired user classes were 
Roofs, Road, Grass, Trees, Water and an additional class called Trail to account for the gravel pathways down the mall 
itself. An additional class called Shadow was also added to account for the fact that shadow areas will be spectrally 
  
See for example, David Landgrebe, "Information Extraction Principles and Methods for Multispectral and 
Hyperspectral Image Data," Chapter 1 of Information Processing for Remote Sensing, edited by C. H. Chen, 
published by the World Scientific Publishing Co., Inc., 1060 Main Street, River Edge, NJ 07661, USA 1999. This 
chapter is also available for download at 
http://dynamo.ecn.purdue.edu/-landgreb/publications.html. 
MultiSpec and its documentation is available for download at 
http://dynamo.ecn.purdue.edu/-biehl/MultiSpec/ 
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188 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000.