Elektronika 2009-11.pdf - Instytut Systemów Elektronicznych

Influence of the number of bins on the recognition
results using Point Distance Histogram
(Wpływ liczby przedziałów w histogramie na wyniki rozpoznawania
z użyciem algorytmu Point Distance Histogram)
dr inż. DARIUSZ FREJLICHOWSKI
Zachodniopomorski Uniwersytet Technologiczny w Szczecinie, Wydział Informatyki
The shape is one of the features of an object that can be used
for its recognition. In the template matching approach a shape
has to be properly represented. It means that it has to be described
in a way making the process of recognition easier.
Usually, the shape description algorithm has to be invariant to
some of its deformations, e.g. scaling or rotation. The most desirable
approaches are robust to all shape deformations. However,
there are not many of that kind, because it is really difficult
to construct an algorithm solving so many various problems.
Moreover, in many cases not all shape distortions arise. Sometimes
the invariance to a few selected problems is sufficient.
Nowadays, the number of shape descriptors applied in the
pattern recognition area is innumerable (an exemplary exhaustive
survey on this topic can be found in [1]). There are
several hundreds various algorithms, Point Distance Histogram
(PDH) being one of them. It was proposed in [2] and
it draws benefits from two very useful solutions: polar transformation
and histogram. It was successfully applied e.g. in
recognition of erythrocyte shapes [3]. The polar transform is
particularly effective in description and recognition of binary
images [4,5]. Thanks to this, the most important property of
the described algorithm is the invariance to selection of the
starting point and rotation (thanks to the usage of histogram),
scaling (thanks to the normalisation) and translation (usage
of the particular point inside an object as an origin of the transform).
Moreover, the method is able to indicate small differences
between similar objects.
The combination of polar coordinates and histogram for
recognition of shapes is not new. Two similar to PDH methods
can be mentioned. The first one is the Distance Histogram -
DH [6]. It calculates the Euclidean distance between the centroid
and all pixels within the object. Every distance is normalized
with respect to the maximal one. The algorithm is very
simple, yet quite effective for example for CBIR applications.
The second proposal: Polar Histogram - PH [7] is almost the
same as the previous one. Only the method for deriving it is
different - it uses transformation from Cartesian to polar coordinates
as more important step. The described solutions are
the most similar to PDH. However, they both work on the
whole shape, with its interior. As it is described in literature
[1,8] the second shape representation - the contour - is possible.
In fact, in the Point Distance Histogram the contour is
used, which makes the algorithm much faster.
At one of the stages during derivation of the shape description
using PDH one has to decide how many bins in a histogram
are used. This parameter is denoted as r. The most
important goal of the experiment described in this paper was
the investigation of the influence of this number on the recognition
results. In order to attain that goal, deformed (rotated
and scaled) trademark shapes were explored. Few examples
of shapes and achieved PDH descriptions for them are provided
in Fig.1.
Description of the Point Distance
Histogram algorithm
The original PDH algorithm uses the centroid as the origin of
the calculations [2]. However, the method is not limited to this
one and if it is desirable any point can be used. This selection
should indicate the name of the descriptor, e.g. in the original
method the complete name is centroid-PDH. The centre of an
object is denoted as O and for centroid it is derived using the
formula [2]:
where: n - number of points in a contour, x i , y i - Cartesian coordinates
of the i-th point.
Having the centre of an object derived we can start the
calculation of the polar co-ordinates: Θ i for angles and Ρ i for
radii [2]:
(1)
(2)
(3)
The values in Θ i are converted into nearest integers [2]:
(4)
Fig.1. Exemplary trademark shapes and PDH descriptions
achieved for them
Rys.1. Przykładowe znaki firmowe i wyznaczone dla nich deksryptory
PDH
The elements in Θ i and Ρ i are now rearranged, according to
increasing values in Θ i , and denoted as Θ j , Ρ j . If some elements
in Θ j are equal, only the one with the highest corresponding
value Ρ j is selected. That gives a vector with at most
360 elements, one for each integer angle. For further work
only the vector of radii is needed. We denote it as Ρ k , where
58 ELEKTRONIKA 11/2009