Elektronika 2009-11.pdf - Instytut Systemów Elektronicznych

k = 1, 2, ..., m and m is the number of elements in Ρ k (m is
less or equal to 360). Then, the normalisation of elements in
vector Ρ k is performed [2]:
The elements in Ρ k are assigned to bins in histogram (ρ k to l k ) [2]:
where r is the predetermined number of bins.
The next step is the normalisation of the values in bins,
according to the highest one [2]:
(5)
(6)
(7)
The examination of the PDH descriptor, using varying value of
the parameter r was performed on binary contour images belonging
to 50 various classes of trademarks, represented in
bitmaps of size 100 by 100 pixels. A couple of examples were
provided in Fig. 1.
According to the template matching approach not affected
contour shapes played the role of base elements. Then, they
were artificially distorted. Three separate tests were performed.
Firstly, the rotation was explored. The angle was selected
randomly. Secondly, the reduction in size (twice). And
finally, scaling up a shape (twice, again).
In each case, deformations were performed on shapes
represented in bitmaps, therefore additionally influence of
noise into the coordinates being extracted during the process
of vectorisation was noticeable.
In all cases one common property was reported. The
recognition rate (RR) was at first increasing rapidly according
to increasing value of r. Then, for r above 8 it was almost stable
and oscillating around 90…95%. After the parameter r had
reached 60 the recognition results became worse. It is clearly
visible in Fig. 2. The best overall average result was RR = 95%
and it was achieved for r = 18, 20, 25, 29, 38 and 51. Because
this result was noticed mainly amongst smaller values of r the
parameter should be taken from them, e.g. r = 18, 20 or 25.
The final histogram representing a shape can be formally written
as a function h(l k ) [2]:
(8)
where [2]:
(9)
Various measures can be used to compare two histograms,
e.g. L 0 , L 1 , L 2 , Matusita, Divergence [9]. In the experiment described
in the following section, the L 2 norm was taken to derive
the dissimilarity between the two descriptions received
using PDH algorithm [9]:
Fig. 3. Recognition rates for rotation and increasing value of r
Rys. 3. Współczynniki rozpoznawania dla obrotu i rosnących
wartości parametru r
(10)
h 1 , h 2 - PDH descriptions being matched, i = 1... r.
Conditions and results of the experiment
Fig. 2. Average recognition rates for increasing value of r
Rys. 2. Średnie współczynniki rozpoznawania dla rosnących wartości
parametru r
Fig.4. Recognition rates for scaling (up and down) and increasing
value of r
Rys.4. Współczynniki rozpoznawania dla skalowania (powiększania
i pomniejszania) i rosnących wartości parametru r
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