*
Q
“~
case this is the evaluation of black and white reproductions of
intensity information in the visible spectrum or any other wave
band. The pixel oriented feature vector then consists of one
component representing a range of grey levels. But there are
only very simple problems, which can be solved in this easy way
(perhaps the separation of water from land in the near infra-
red wave band).
An extension of this method can be achieved by the combined com-
putation of more than one wave band (channel). Now the feature
vector assigned to the pixel is of fixed length according to
the number of channels used. Each component refers to a distinct
range of grey levels in the corresponding wave band. The question
how many channels in which parts of the spectrum should be used
depends on the problem and the system capacity and is in gene-
ral not yet solved.
The implemented systems for multispectral analysis often use
3to 4 wave bands. But there are also sensor Systems, which re-
cord up to 12 or 24 channels. In many applications this high
quantity of spectral information cannot be fully utilized by
multispectral analysis. The merit of a great number of Qifrevens
wave bands has to be compared with the increase in the processing
costs for feature extraction, especially because the amount of
redundancy is growing with the number of channels used and the pro-
fit of accuracy may not justify the essential higher expense of
computation time and storage. On the other hand the selection of
a subset of channels may include a loss of significant informa-
tion.
The concentration of the nonredundant information in the multi-
spectral densities of different wave bands can be achieved by
applying a density transformation. Multispectral data is inhe-
rently strongly correlated and tends to distribute itself with
an elongated shape in the n-dimensional space of different chan-
nels. Therefore, the greatest majority of data variability may
be concentrated on a small number of axes and a technique of
- 18 -
principal components transformation appears to yield excellent
results. Such a transformation is known as Karhunen-Loeve's
orthogonal expansion, employed in data compression /25, 26/.
It consists of defining a new coordinate system, obtained by
a linear combination of the original coordinates, referred to as
transformation in the direction of principle components.
For density transformation the procedure is as follows: the first
axis is chosen as to be oriented along the largest dispersion
range; the next axis is chosen perpend icularly to the first
and again along a direction of the next largest dispersion range,
and so forth.
In figure 19 the eigenvalues of an actual 12-channel multispec-
tral data set are Shown. In this case an eigenvalue is an indi-
cator of the relative range of the data after pricipal components
tranformation. Even though there have been 12 channels before
transformation only three principal values have a sufficiently
wide range as to yield a real information contribution. The range
in these signif icant Principal components is essentially greater
than the range in the original spectral bands and therefore in-
cludes greater potential for resolution and contrast.
The possibility to gain features by evaluation of isolated pixels
is very limited. Extensive information can be computed from the
intensity distribution within a neighbourhood of the pixel being
regarded. This can be done by a local transformation of the ori-
ginal or preprocessed data, whereby this transformation may be
understood as a Preprocessing step itself. In this case the two-
dimensional grey level image will be transformed into a matrix
of the same dimension and Size, where the elements e.g. repre-
sent contour information, which can be brought into relation
with the corresponding pixel in the original image.
The extraction of Such contour information can be accomplished
in different Ways. One of the most primitive methods is the two-
dimensional differentiation of an image. For each pixel the pro-
