7A-5-6
Figure 9: (a) An octagon imager(b) 10 magnitudes of
Figure 8: Detected signs from original images shown NFD of an octagonr(c) a circle imager(d) 10 magni-
in Figures 5(a) r6(a)rand 7(a) tudes of NFD of a circle
Once boundaries of the color regions are trackedr
points (x, y) on the boundary can be expressed as com
plex numbers.
Z{ A) = x(A) + iy( A)
(a) (b) (c) (d)
where A is the arclength.
The Fourier descriptor is thus the DFT of the se
quence of complex numbers.
Figure 10: (a) A diamond imager (b) 10 magnitudes
of NFD of diamondr(c) a square imager(d) 10 mag
nitudes of NFD of a square
F u
1
N
N/ 2-1
^2 z n exp
n=-N/2
2ni
TNT
. n
To eliminate the dependency on positionTsize Tand
orientation of the objectsTthe Normalized Fourier de
scriptors (NFD) [8] are used. To identify the shape of
the boundaryrnormalized Fourier descriptors of regu
lar shapes are computed and stored first. If the nor
malized Fourier descriptor of the tracked boundary is
matched to a regular shape’s NFDrthen the bound
ary has that shape. In our experimentsTpartial mag
nitudes of NFDrF (—6)T F (-5)T F (-4)rF (-3)T
F (—2)TF (2)TF (3)r F (4)r F (5)T F (6)rthe ten
coefficient's of NFD of each model is used as features
which are shown in Figure 9-13. In practiceTwe can
found that the normalized Fourier descriptors of a oc
tagon are similar to that of a dreier and the case
is the same for the upper semi-circle and the lower
semi-circlerthe upper triangle and the down triangle.
To further discern these pairsTrelative position of the
edges can be used. For examplera down triangle has
two slanted edges under a horizontal edge.
To get good NFD of the tracked boundaryr a
smoothing function can be applied to the tracked
boundary and a polygonal approximation can be used
to refine the exact shapes.
Figure 11: (a) A lower semi circle imager(b) 10 mag
nitudes of NFD of a lower dreier (c) an upper semi
circle imageT (d) 10 magnitudes of NFD of an upper
semi circle
Figure 12: (a) A down triangle imager(b) 10 magni
tudes of NFD of a down triangler(c) an upper triangle
imageT(d) 10 magnitudes of NFD of an upper triangle
