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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