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Spectral Image Analysis 259

of spectral similarity, euclidean spectral distance can serve as a mem-
bership function. If a pixel has a shorter distance to the center of one
cluster than to the center of another, then it is more likely to be a
member of the former cluster because it shares a higher spectral sim-
ilarity with all the pixels in that cluster.

7.2.2 Mahalanobis Spectral Distance
Also called Manhattan distance in human geography the mahalano-
bis distance is the algebraic sum of the absolute differences between
two pixels in the same band and in every band used in the classifica-
tion (Fig. 7.3). This distance, D , is calculated using Eq. (7.2). The use
m
of the absolute value eliminates the need to worry about which pixel
value should be subtracted from which pixel in deriving the differ-
ence. Since the difference is guaranteed to be positive, no differences
are going to negate themselves in the summation.

m ∑
D = n | DN − DN | (7.2)
Bi
Ai
i=1
The mahalanobis spectral distance is easier to compute and less
complex than the euclidean distance. It remains unknown which
distance is able to produce more accurate results, D or D , even
e m
though the euclidean spectral distance is used much more commonly
in practice.

255
Pixel B
(DN , DN )
B1
B2
DN (Band 2) ΔDN = DN B2 – DN A2

2

Pixel A
(DN , DN A2 ) ΔDN = DN B1 – DN A1
A1
1
0
0 255
DN (Band 1)
FIGURE 7.3 Calculation of the mahalanobis distance in the spectral domain.
It is the sum of the two right sides of the right triangle as against the inclined
side which is the euclidean distance.