etc. principal component (PC1, PC2,...), denoted by y XNosya» (Ye The
: Y : : E n
new images contain the same information as the original OneB, however
concentrated in the first component (PC1), to a lesser extent in the se-
cond component (PC2) and so forth. Hardly any information is contained
in the higher order components. "Information" thereby is variation of
gray tone corresponding to transformed radiance levels, or in another
context the significance of the pattern apprearing on the image for in-
terpretation.
The transformation from x. to y. is rather simple, consisting for each
pixel of a weighted average Of each spectral dimension i:
„= Dn.. X, Fü. XA, T... t 4. X
Ji 31 1 12 2 in n
The weights (coefficients a..) form a rotation matrix which diagonalizes
a covariance matrix estimated over a subset of the image either selected
automatically or specified by the interpreter. Many discussions of the
method exist, e.g. Landgrebe et al., (1972), Ready and Wintz (1973),
Mulder and Hempenius (1974) and Anuta (1977).
The advantage of PCT applied to MSS data is twofold:
(a) An effective compression of the data is achieved. For the example
of the 4 channels of Landsat, almost all information is contained
in the first two principal components. With aircraft MSS, a drastic
reduction from e.g. 12 channels to the first few PC's is possible.
(b) This reduced dimensionality allows the operator to define, on the
basis of a proper sample set, the best products for interpretation
(compare section 4.3).
With Landsat, PCT has shown valuable results not only by dimensiona-
lity compression, but also as a method of enhancing certain phenomena.
In the view of some image processing experts, however, results of PCT
are somewhat unpredictable.These experts may call it a hit or miss tech-
nique.The so-called deficiencies of PCT relative to information extraction
can be alleviated by the addition of training: The image is appropriately
sampled using interpretation expertise and the PCT is based on the manually
selected sample. One may rightfully generalize that image processing tech-
niques should always be applied under the control of the interpreter and
that without such control (training) most methods are hit or miss techniques.
Transformations that maximize the variation between identified class means
in certain of the transformed components have been termed canonical
and have been applied successfully to the geologic analysis of multi-
spectral images (Podwysocki et al., 1977). Linear discriminant analy-
sis procedures have also been used effectively to deal with a large
multispectral data base (Siegal and Abrams, 1976; Jennrich, 1977).
4.2.2 Ratioing
Enhancement of multiple, in particular multispectral images using
ratio Bj/Bj of spectral bands i, j has been extensively applied in
planetological interpretation of lunar images (Bi, Bj are gray values of
bends i, j). These methods can be analog using photographic techniques
(Mulder and Donker, 1977). With the advent of digital data ratioing is
applied digitally to remove effects of the spectral brightness, leaving
entirely the
spectral differences. Thus hill shadow (variations of