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ERDC TR-05-1

Ln = natural logarithm function

This maximum likelihood equation, including notations and descriptions for

There are a number of slightly different versions of the maximum-likelihood

classifier published in various multivariate statistical textbooks and image proc-

essing textbooks. All variations calculate the same weighted distance estimate

(*D*) for every pixel. Actually, *D *is calculated *c *times for each pixel; that is, if

there are five classes, then *D *is calculated five times for every pixel. The

weighted distance estimates for a single pixel are then sorted, with that pixel as-

signed to the class with the lowest *D *value (i.e., the smallest weighted distance).

have multivariate statistics to calculate several variables in the equation above,

including: *M*c, ac, and *Cov*c. The multivariate statistics represent a priori informa-

tion and, therefore, train the classification algorithm concerning the means and

ranges of pixel values that define each class. These training statistics were gener-

ated from the 36 training sites (i.e., the sample plots). Using ERDAS *Imagine*, we

extracted pixel values (integer values for each of the four CAMIS spectral bands)

from the December 2001 CAMIS images at each sample site by navigating to the

X,Y coordinates collected in the field. Typically, at least 25 pixels composed the

training site. The training pixel values were stored in a separate database. Train-

ing statistics were then generated from each of the 36 sample sites. A number of

plots were replicates of the same vegetation type. These statistics were combined

to generate a total of 24 initial spectral signatures.

signatures as training data to the CAMIS mosaic, the signatures were evaluated

for separability. Signature separability is a standard tool in commercial image

processing software packages. The Transformed Divergence algorithm was used,

although a variety of algorithms are available within *Imagine*. The four-dimen-

sional mean vectors and covariance matrices are computed for the training sta-

tistics. A transformed divergence score is calculated to estimate the magnitude of

the pair wise differences, or separabilities, of each of the 24 class mean vectors.

The results of the signature separability tests highlighted those signatures that,

while supporting unique vegetation species associations (as observed in the

field), were not distinct with respect to their spectral properties. The lack of sepa-

*