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96 Application Examples in the Vision Domain

and rotated freely. The goal is to determine the proper shift and twist angle
parameters when at least two image points are seen. Furthermore we de-
sire to predict the locations of the hidden – maybe occluded or concealed –
features. For example, this can be helpful to activate and direct specialized
(possibly expensive) perception schema upon the predicted region.

α
ζ
δ
ε β
η
γ

Figure 7.1: The star constellation the “Big Dipper” with its seven prominent stars

, and . (Left): The training example consists of the image position

of a seven stars

in a particular viewing situation. (Right): Three
examples of completed constellations after seeing only two stars in translated
and rotated position. The PSOM output are the image location of the missing
stars and desired set of viewing parameters (shift and rotation angle.)
Fig. 7.1 depicts the example. It shows the positions of the seven promi-
nent stars in the constellation Ursa Major to form the asterisk called the
“Big Dipper”. The positions (x y ) in the image of these seven stars ( )
are taken from e.g. a large photograph. Together with the center-of-gravity
position x c c and
y the rotation angle of the major axis ( - ) they span the
y

embedding space X with the variables x fx c c y
y y x x g . x

As soon as two stars are visible, the PSOM network can predict the
location of the missing stars and outputs the current viewing parameters –

here shift and rotation (x c c y). Additionally other correlated parameters
of interest can be trained, e.g. azimuth, elevation angle, or time values.
While two points are principally enough to fully recover the solution
in this problem any realistic reconstruction task inevitably is faced with
noise. Here the fusion of more image features is therefore an important
problem, which can be elegantly solved by the associative completion
mechanism of the PSOM.