Page 298 - Digital Analysis of Remotely Sensed Imagery

260 Cha pte r Se v e n

7.2.3 Normalized Distance
Normalized distance, D , refers to the absolute value of the differ-
norm
ence between the means of two clusters divided by the sum of their
standard deviations (Swain, 1978), or

| u − u |
j
i
D = (7.3)
norm δ +δ
i j
where u and u are the means of the two clusters and d and d are their
i j i j
corresponding standard deviations.
This distance applies to two clusters of pixels, but not individual
pixels. The distance is measured from the center of one cluster to that
of another. There is no restriction as to how many members each clus-
ter can contain. Virtually, this distance is indicative of the statistical
separability between the two clusters. The larger the distance, the
more easily and accurately the two clusters can be distinguished from
each other. This distance may be used to judge the quality of the
selected training samples between any two covers before these sam-
ples are formally used in a classification.

7.3 Unsupervised Classification
Unsupervised classification is essentially clustering analysis in
which pixels are grouped into certain categories in terms of the
similarity in their spectral values. In this analytical procedure, all
pixels in the input data are categorized into one of the groups
specified by the analyst beforehand. Prior to the classification, the
image analyst does not have to know anything about either the
scene or the covers to be produced. During posterior processing
the identity of each spectral cluster is scrutinized and may be
linked to a meaningful ground cover. Unsupervised classification
may be implemented in a variety of ways. This section presents
four common approaches.

7.3.1 Moving Cluster Analysis
Also known as K-means clustering, moving clustering starts with the
specification of the total number of spectral classes (e.g., k) to be clus-
tered from the input data. Then the computer arbitrarily selects this
number of cluster centers or means as the candidates. The distance of
every pixel in the input image to each of the candidate clusters is
calculated. Of all the euclidean spectral distances calculated, a pixel is
assigned to a candidate cluster to which the spectral distance is the
shortest. After all of the pixels in the input image have been assigned
to one of the candidate clusters, the sum of squared error (SSE) is