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Example: Line Fitting

Figure 5.5
shows how the FHT works for , when parameter space is a plane,
hyperplanes are straight lines and hypercubes are squares whose associated
hyperspheres are circles passing through the vertices of the squares
(figure 5.5).
This is applicable to the
problem of finding a straight line through points on a plane. If the
plane has coordinates the line can be written

where and are constant. Each point
votes for a line in parameter space:

Let the initial ranges of and , defining the root
hypercube, be and
centred around and respectively.
Then the above equation can put in the form of
equation 5.15 using the transformation

where
.

2006-03-17