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Logo Recognition by Dan Chen, Lizhe Wang, Jingying Chen

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7
Logo matching
CONTENTS
7.1 Hausdorff distance ........................................................ 98
7.2 Modified LHD (MLHD) ................................................... 100
7.3 Experimental results ...................................................... 105
7.3.1 Matching results ................................................... 107
7.3.2 Degradation analysis .............................................. 113
7.3.3 Results analysis with respect to the LHD and the MHD ......... 113
7.3.4 Discussion and comparison with other methods .................. 117
7.4 Summary .................................................................. 120
As stated in Chapter 3, there are five main shape recognition methods (i.e.,
statistical approach, syntactic/structural approach, template matching, neu-
ral network, hybrid method). However, not all methods are appropriate for
each type of shape and application, i.e., the method of choice depends on the
properties of the shape to be described and the particular application. The
presence of noise can also influence the choice of method. Since the structural
approach is based on the local shape features and robust to the noisy condi-
tion while template matching can achieve a high recognition rate, a hybrid of
structural and template matching can show strong potential for shape match-
ing. Sternby [193] presented a structurally based template matching method,
which utilizes the explicit structure of the samples to model the non-linear
global variations by a set of affine transformations through a structural repa-
rameterization. Bruneli and Poggio [18] argued that successful object recog-
nition approaches may need to combine aspects of structural feature based
approaches with template matching methods. Based on these observations,
a hybrid method combining the structural approach and template matching,
i.e., the modified Line Segment Hausdorff Distance (LHD), is presented for
logo matching in this study.
After the indexing process, the test logo is matched to all the likely mod-
els in a line-to-line matching manner. The matching is implemented as a dis-
similarity computation process. In this chapter, the modified Line Segment
Hausdorff Distance (LHD) measure is proposed to match logos. The proposed
approach has better distinctive capability (especially for broken lines) than
the original LHD. Compared with other researches on logo recognition, this
approach has the advantage of incorporating structural and spatial informa-
tion to compute the dissimilarity between two sets of line segments rather than
97
98 Logo Recognition: Theory and Practice
two sets of points. The added information can conceptually provide more and
better distinctive capability for recognition.
7.1 Hausdorff distance
The Hausdorff distance is one of the commonly used measures for shape match-
ing. It is a distance defined between two sets of points [173]. Unlike most shape
comparison methods that build a one-to-one correspondence between a model
and a test image, the Hausdorff distance can be calculated without explicit
point correspondence. Huttenlocher et al. [88] argued that the Hausdorff dis-
tance for shape matching is more tolerant to perturbations on the locations of
points than binary correlation techniques since it measures proximity rather
than exact superposition. Also, the Hausdorff distance is simple in concept
and easy to implement.
GiventwosetsofpointsM = {m
1
, ..., m
p
} (representing a model in the
database) and N = {n
1
, ..., n
q
} (representing a test image), the Hausdorff
distance is defined as
H(M,N)=max(h(M, N),h(N,M)) (7.1)
where
h(M,N)= max
m
i
M
min
n
j
N
m
i
n
j
(7.2)
and ·is some underlying distance function for comparing two points m
i
and n
j
(e.g., the L
2
or Euclidean norm). The function h(M,N) is called the
directed Hausdorff distance from M to N. It identies the point m
i
M that
is the farthest from its nearest neighbors in N. Thus, the Hausdorff distance,
H(M,N), measures the degree of mismatch between two sets. Intuitively, if
the Hausdorff distance is d,theneverypointofM must be within a distance
d of some point of N and vice versa. Belogay et al. [12] used the Hausdorff
distance to compare curves. A method using the Hausdorff distance for visually
locating an object in an image was developed in [172].
Dubuisson and Jain [49] investigated 24 forms of different Hausdorff dis-
tance measures and indicated that a Modified Hausdorff Distance (MHD)
measure had the best performance. The directed MHD is defined as
h(M,N)=
1
p
m
i
M
min
n
j
N
m
i
n
j
(7.3)
where p isthenumberofpointsinM. The definition of the undirected MHD
is the same as (7.1).
The Hausdorff distance defined in (7.1) and (7.2) is very sensitive to outlier
points. A few outlier points, even only a single one, can perturb the distance

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