data base of true and false targets. Filtered images are correlated
and cross correlated to determine the most discriminating frequencies.
In practice, this process is too time consuming. Certain assumption
are reasonable in spatial filtering. It is reasonable to assume that
the reference and test images do not have much more detail than is
absolutely necessary to distinguish the true target. To reduce the
number of points needed in the digital imagery, the original sampling
process was accomplished by limiting the spatial frequencies to those
required to recognize the target. Thus, the appropriate filter to
eliminate unnecessary frequency components will have the form of a
high-pass filter. The nature of this high-pass filter is dependent on
the application of the matched filter.
The matched filter is created for a specific target. If the
target is present, the correlation is larger than for areas of the
image where the target is absent. If the target changes slightly from
the reference stored on the filter, the correlation drops. In a
practical application, small changes in the expected target are the
rule rather than the exception. If the target grows in size, rotates,
or changes its appearance slightly, the correlation may drop below the
threshold. This topic will be discussed further in Chapter V, but it
is necessary to point out that the invariance of the filter to small
changes in the target depends heavily on the frequencies used in the
correlation. Using the previous example, recall that the high-pass
images showing the edges allowed discrimination between the square and
circle. If the square were rotated slightly, the results would
change. The cross-correlation between a square and a slightly rotated
square depends on the frequencies used in the correlation. If only