the case of the affine-invariant coordinates an af-
fine mapping becomes apparent in expressions in
which the determinant of the transformation ma-
trix T is involved. The invariance of x(7) can
be shown by an explicit analytical computation
in the course of which the determinant detT is
eliminated. A certain problem results from the
fact that the curve, i.e. the border line of the
region of interest, is discrete. The affine length
is not suited for a parameterization of a polygon.
A simple way out of this problem is to use a sli-
ding polynomial of degree n that approximates
the polygon.
At a first glance the procedure seems to be very
promising. To evaluate this experimentally the
affine-invariant curvature of a triangle, a rec-
tangle and a circle are calculated and plotted in
figure 3. Picture (a) shows the results derived
ei N (a)
= IN
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rete
me Q
Figure 3: Affine-invariant curvature of a triangu-
lar, rectangular and circular shaped contour
from the original figures. In (b) these figures are
distorted by affine transformation and in (c) noise
is added. The comparison of the plotted curva-
tures of (c) with respect to (a) and (b) indica-
tes the drawback of the procedure. Though only
small noise is added (compare the drawn figures)
the affine-invariant curvature changes considera-
bly. The main reason for this noise sensitivity is
that second derivatives are involved in the calcu-
lation. Because of the noise sensitivity this pro-
cedure in not considered further.
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