Binary Pattern Matching from a Local Dissimilarity
Measure
Fre´de´ric Morain-Nicolier1, Je´roˆme Landre´1, Su Ruan1
1 CReSTIC-URCA, 9 rue de Que´bec, IUT, 10026 Troyes Cedex, France
e-mail: frederic.nicolier@univ-reims.fr
Abstract— This communication deals with finding the position
of a reference shape in a given image. The proposed matcher
is constructed from local dissimilarity maps. These maps allow
to efficiently and robustly measure the differences between two
images. It is shown an example that the matcher potentially
returns less false-positives than a reference method (chamfer
matching). This is possible as the local dissimilarity measure is
symmetric, which makes it more robust to noise. We show that the
proposed matcher is a generalization of the chamfer matching.
It also allows fast computation times. A good robustness to noise
is confirmed from presented simulations.
Keywords— Pattern recognition, template localization, chamfer
matching, local dissimilarity.
I. INTRODUCTION
The field of shape matching is a key step in a visual
recognition system. Shape matching is a subset of image
registration methods [11]. In this case, the pattern is classically
a binary image where foreground pixels represent the shape.
Logo recognition or video coding are ones of the many
applications of this domain. The usual process starts with a
segmentation or a binarization to extract the object pixels.
The object is described by a set of features. A comparison
with some reference features is performed. A decision is taken
using a similarity measure between these features [9].
Other algorithms represent the object by a template. Cham-
fer matching [3] is a technique for finding the best fit of
edge points from two different images, by minimizing a
generalized distance between them. The original idea has
several good properties but also suffers false matching [5].
Borgefors proposed an improved algorithm with fewer false
matching by selecting an average of the root mean squared
values for the matching measure. The high computation times
are lowered with a multi-resolution approach. Another popular
matching method is the Hausdorff distance [6] or one of its
variants [1].
In previous works [2], we have designed a local dissimilarity
measure leading to a Local Dissimilarity Map (LDM). This
map is computed using sliding windows with an auto-adaptive
size. Here is the general idea: if the pixels in the sliding
window belong to coarse information, the window is grown
to be big enough to grasp the local information. The LDM
only allows to compare binary images, but without any feature
extraction. Some pre-processing can thus be avoided.
In relation with this, a shape matcher is built from the
LDM. The searched shape is coded in a binary pattern. This
pattern is locally compared to image pixels thanks to the LDM.
The LDM is reformulated with linear operations in section
2. Section 3 is dedicated to the construction of the matcher
from the LDM. The LDM-matcher and the Borgefors chamfer-
matching are compared in an example in section 4 and on a
large set of noisy patterns in section 5.
II. LOCAL DISSIMILARITY MAP REFORMULATION
Among distance measures over binary images, the Haus-
dorff distance (HD) has often been used in the content-based
retrieval domain and is known to have successful applications
in object matching [6]. The HD is defined by
HD(A;B) = max(h(A;B); h(B;A)) (1)
with h(A;B) = maxa2A(minb2B d(a; b)) where d is an
underlying distance. This is a global distance. We have pro-
posed a local measure and a local dissimilarity map (LDM)
computed with an iterative algorithm [2]. Intuitively, the local
computation window is grown to be big enough to grasp the
local information. The good behavior of the LDM has been
shown with a Content Based Image Retrieval (CBIR) task :
retrieve ancient illustrations representing the same scene. We
have also proposed a LDM formula allowing fast computa-
tions, by removing the explicit iteration in the algorithm. For
binary images, the LDM is thus:
LDMA;B(p) = jA(p)B(p)jmax(dtA(p);dtB(p)); (2)
where dtX is the distance transform of X . The distance
transform values are obtained for each pixel, by computing
the distance to the nearest non-zero pixel (foreground). It can
be very efficiently computed with a chamfer distance, which
is a very good euclidean distance approximation. Moreover it
can be computed faster in a two pass algorithm [7].
Still for binary images, equation (2) can be even more
simplified in:
LDMA;B = BdtA +AdtB : (3)
This new equation is of big interest due to max and abs opera-
tors removal. Linear processing operations such as convolution
product are thus possible.
Proof: The proof is quite forward. LDM1 (resp. LDM2)
is LDM from eq. (2) (resp. eq. (3)). For a given pixel p, there
are few alternatives :