In PAMI1999, the notion of
the histogram of forces is introduced. Such a histogram constitutes a
fuzzy qualitative representation of the relative position between two
objects. We demonstrate that the force histogram generalizes and
supersedes the angle histogram. In particular, the histogram of
constant forces coincides with the histogram of angles, but without its
weaknesses (long processing times, anisotropy, requirement for raster
data...). The two histograms are fundamentally equivalent, even though
the first arises from the continuous case and the second from the
discrete case. The movie below shows two rectangular objects, and the
histograms associated with these objects. Different sets of directions
are considered (the number of directions corresponds to the number of
values that represent each histogram). The largest set contains 10000
directions and the smallest one only 8. Note that the intrinsic form of
the histogram of angles only appears when few directions are
considered. The shape of the force histogram is remarkably stable.
