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Logo Recognition by Dan Chen, Lizhe Wang, Jingying Chen

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6
Logo indexing
CONTENTS
6.1 Normalization ............................................................. 81
6.2 Indexing ................................................................... 83
6.2.1 Reference angle indexing (filter 1) ................................ 85
6.2.2 Line orientation indexing (filters 2 and 3) ........................ 85
6.2.2.1 Histogram representation ................................ 86
6.2.2.2 Histogram comparison ................................... 87
6.2.3 Experimental results .............................................. 88
6.2.3.1 Retrieval results .......................................... 91
6.3 Summary .................................................................. 96
When the number of test and model logos is large, the price for brute force
matching between the test and model logos is high. To cut down the CPU
time, one can do logo indexing in order to narrow down the scope of matches.
Logo indexing operates on the normalized Line Segment Maps (LSM) of logos
and produces a moderate number of likely models with respect to a test logo.
The normalized LSM is generated from a normalization process that aligns
logos to a standard position and scale. All the models can be pre-aligned to
save time. Details of the processes are described in the following sections.
6.1 Normalization
This process transforms a model or test pattern into its corresponding normal
form such that it is invariant under translation, scaling and rotation. There
are a number of techniques on shape normalization, such as moment invari-
ants [210], Fourier descriptor [225], Hough transformation [8], shape mean
and norm [78], shape matrix [196], morphological transformation [212] and
Radon Composite features [34]. Jiang and Tomasi [96] presented shape nor-
malization based on implicit representations; they adjusted the influence of
the different shape parts using a weight function. Schreiber and Bassat [181]
used the gravitation center of the contour of the object as a single anchor
point to align the image and then compared the images by string matching.
Arica and Yarman-Vural [3] normalized the shape to a fixed size window, in
81
82 Logo Recognition: Theory and Practice
order to make the shape recognition system size invariant and comparable.
The size of the window, the number of scanning directions and the number of
regions in each scanning direction are the normalization parameters. However,
these methods are not robust to occluded test images. Hence, Govindu et al.
[74] employed the geometric properties of image contour to align images. They
recovered transformations between the images using the statistical distribu-
tion of geometric properties. This method is robust to problems of occlusion,
clutter and errors in low-level processing.
In this study, the normalization can be obtained by transforming and scal-
ing all the model and test logos to a standard location. It is based on the
distinctive lines, which are long and form sharper angles with their immediate
neighbors, from a logo. The details of the normalization process are described
in the following:
Step 1: Select distinctive lines from a logo. In order to determine whether a
line, l
i
, (see Figure 6.1) is distinctive or not, we define a figure of merit g
i
to measure its distinctiveness as
g
i
= L
i
f(θ
A
)f(θ
B
) (6.1)
FIGURE 6.1: Two examples of measuring the line distinctiveness.
where L
i
is the length of line l
i
,anglesθ
A
and θ
B
are measured from l
i
to
l
j
and l
k
, respectively, in a counter-clockwise manner. f(θ) is a function of
θ; it is a measure of angle sharpness.
f(θ)=| π θ | 0 θ 2π (6.2)
According to this computation, a sharper angle will give a larger value of f.
Hence, a long line with sharp angles will result in a large g
i
(i.e., desirable),
whereas a short line with obtuse angles will result in a small g
i
(i.e., not
desirable). The above discussion can be summarized as:
(1) determine f(θ
A
)andf(θ
B
) for each line.

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