June 2014
Intermediate to advanced
576 pages
16h 43m
English
book
Image Analysis, Classification and Change Detection in Remote Sensing, 3rd Edition
by Morton J. Canty
Content preview from Image Analysis, Classification and Change Detection in Remote Sensing, 3rd Edition
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236 Supervised Classification Part 1
FIGURE 6.3
ROIs for supervised c lassification. The insert shows the training observations
projected onto the plane of the first two principal axes. (See color insert.)
cova riance matrices Σ
1
= Σ
2
, then it can be shown that the minimum in fact
occurs at s = 1/2. Approximating the minimum as s = 1/2 also for the cas e
where Σ
1
6= Σ
2
leads to the (somewhat les s tight) Bhattacharyya bound ǫ
B
,
ǫ ≤ ǫ
B
=
p
Pr(1)Pr(2)
Z
p
p(g | 1)p(g | 2) dg. (6.11)
This integral can be evaluated explicitly (Exercise 1). The result is
ǫ
B
=
p
Pr(1)Pr(2) e
−B
,
Training data and separability 237
where B is the Bhattacharyya distance, g iven by
B =
1
8
(µ
2
−
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