ACCURATE SIMILARITY MEASURES FOR SILHOUETTES

RECOGNITION

Saliha Aouat and Slimane Larabi

LRIA Laboratory, Computer Science Department,

University of Sciences and Technology – Houari Boumediene, Algiers, Algeria

Keywords: Textual Descriptors, Noise, Similarity Measures, Indexing, Recognition, Quasi-invariants, Parts Areas.

Abstract: In this paper, we propose a new method to recognize silhouettes of objects. Models of silhouettes are stored

in the database using their textual descriptors. Textual Descriptors are written following the part-based

method published in (Larabi et al, 2003). The main issue with the textual description is its sensitiveness to

noise, in order to overcome this issue, we have applied (Aouat and Larabi, 2010) a convolution to initial

outline shape with a Gaussian filter at different scales. The approach was very interesting for shape

matching and indexing (Aouat and Larabi, 2009), but unfortunately it is not appropriate to the recognition

process because there is no use of similarity measures in order to select the best model for a query

silhouette.

In this paper, we compute parts areas and geometric quasi-invariants to find the best model for the given

query; they are efficient similarity measures to perform the recognition process.

1 INTRODUCTION

There are two general methods for image matching,

retrieval and recognition: intensity-based (color and

texture) and geometry-based (shape), (Alvarado et

al, 2002; Arandjelovic and Zisserman, 2010; Chang

and Kimia, 2011; Keysers et al, 2007; Latecki et al,

2005; Ma and Latecki, 2011; Mokhtarian, 1995).

Our method is a geometry-based since we use

parts of 2D silhouettes, and an appearance-based

method, because we use different views of 3D

objects.

In this paper, we propose a new approach to

recognize descriptors of 2D silhouettes. The

silhouette is represented with a single closed contour

(Larabi et al, 2003). We used textual descriptors of

silhouettes for the matching and the indexing

processes (Aouat and Larabi, 2009). Due to noise,

the descriptors may be very different even though

the silhouettes look alike. Comparing such

silhouettes descriptors will result in a mismatch, for

this reason an algorithm was developed to smooth

the outline shapes (Aouat and Larabi, 2010).

In this paper, we assume that the smoothing and

the indexing processes were already performed

(Aouat and Larabi, 2010; Aouat and Larabi, 2009),

and we compute efficient similarity measures to

complete the recognition process.

The paper is structured as follows:

In the second section, we give an overview of the

outline shapes part-based method (Larabi et al,

2003). In the third section, we will explain the

necessity to compute similarity measures after the

indexing process. In the fourth section however, the

first similarity measure based on parts areas will be

presented, followed, in the fifth section, by the

second similarity measure based on Geometric

quasi-invariants, we will also validate the quasi-

invariants values we maintain for the recognition

process. In the last experimental section, we use real

images of two well known databases and discuss the

descriptors matching and recognition after applying

both similarity measures on textual descriptors of

used silhouettes.

2 TEXTUAL DESCRIPTION OF

SILHOUETTES

The part based method (Larabi et al, 2003) builds

shape descriptors by using the minimum rectangle

(MR) that encloses the outline shape (Graham,

1972). (OXY) is the referential attached to MR

chosen such as the origin O is the left top edge of

MR (see Figure 1).

397

Aouat S. and Larabi S..

ACCURATE SIMILARITY MEASURES FOR SILHOUETTES RECOGNITION.

DOI: 10.5220/0003815303970400

In Proceedings of the International Conference on Computer Vision Theory and Applications (VISAPP-2012), pages 397-400

ISBN: 978-989-8565-03-7

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

Figure 1: Initial silhouette, the minimum rectangle MR,

and the rotated silhouette

From this geometric description, the outline shape

may be drawn without ambiguity implying the

propriety of uniqueness and preservation of

perceptual structure. The invariance of this

description to rotation is guaranteed by the sweep up

of the silhouette following one of the directions of

the minimum rectangle encompassing the silhouette.

For more details refer to (Larabi et al, 2003).

Textual descriptors of silhouettes are sensitive to

noise; indeed noise may modify and distorts the

outlines and their descriptors such as shown in

Figures 2 and 3.

Figure 2: A non-noisy silhouette and its decomposition.

Figure 3: A noisy silhouette and its decomposition.

The coarse descriptor of the silhouette in Figure

2 is:

while

the coarse descriptor of the silhouette in Figure 3

was:

<CP><CP>P1 P2 J1 P3 </CP> D1 P4 P5</CP>.

3 INDEXING PROCESS

The database of shapes models, represented by their

textual descriptors, is indexed using the following

data as shown in Figure 4:

The index is: (5, 1, 1, 01, 3, 3, wjjh&wjjw)

where: (5 is the number of parts, 1 is the number of

junction lines, 1 is the number of disjunction lines,

01 indicates that there is a junction line followed by

a disjunction line, 3, 3 indicate respectively that

there are three parts in relation with the first and the

second separating lines. The set of characters

wjjh&wjjw indicates that in the first separating line,

there are four segments with attributes w, j, j, h and

in the second separating line, there are four segments

with attributes w, j, j, w.)

Figure 4: Indexing a shape.

Different shapes may have the same index, the

difference between them is in the geometry of their

parts. In order to perform the full matching for the

recognition process, two similarity measures will be

used: the Parts Areas and the Geometric Quasi-

invariants.

4 PARTS AREAS

Let us consider the two curves f and g shown in

Figure 5. If f tends towards g (f ~ g) then the area

between f and the (OX) axis will be approximately

the same area as that between g and the (OX) axis.

In this case the difference between the two areas is

close to zero. As the shape is included into the

Minimum Rectangle (MR) which is the referential

OXY (see Figure 1), so all (OX) and (OY)

coordinates are positive therefore we can write:

b b

| ∫

f(x) dx - ∫

g(x) dx | ~ 0

All selected models after the indexing process,

will have the same index as the query, so they will

evidently have the same number of parts. The query

silhouette will be compared with all models of its

class that have the same index and the same number

of parts. The recognition aims to select the best

model which is close to the query.

Figure 5: Difference of areas between two curves.

The first step consists in reconstructing

VISAPP 2012 - International Conference on Computer Vision Theory and Applications

398

silhouettes from their descriptors. In the second step,

we use the same referential for both query and

model silhouettes, this is possible due to the use of

the minimum rectangle as the referential. The last

step is the computation of the areas:

Let us consider two vectors V

q (Sq1,Sq2 ,…Sqn )

and Vm (Sm1,Sm2 ,…Smn) containing respectively

parts areas of the query and those of the model.

The first similarity measure between two

silhouettes is given by:

∑ (S

mi-Sqi)

i=1

where n is the number of parts of both

silhouettes. The best selected model is that which

minimizes this similarity measure.

5 QUASI-INVARIANTS

The Geometric quasi-invariants (ρ, θ) are defined as

the angle θ between the intersecting segments, and

the segments length ratio ρ, (see Figure 6).

=ρ

2010

arccos

aaaa

=θ

Figure 6: Geometric quasi-invariants (ρ , θ ).

The (ρ, θ) pairs found in each image vary

slightly with a small change in the viewpoint, and

are invariant under similarity transform of the image

(Gros, 1994; Lamiroy and Gros, 1996).

In order to study the variation of the pair (ρ, θ)

between successive segments, we considered, in an

offline study, 28 polyhydric objects and several

images (856 images) of each object taken under

different points of view (average object rotation is

). Identical views have been eliminated of the

image base to avoid redundancy. We then extract the

geometric features: that are the intersecting

segments and we analyze the similarities to

determine the similarities values. We use ln(ρ)

instead of ρ because ln(ρ) follows a uniform

distribution. For each two successive images of the

rotated object, we analyze identical geometric

configurations and evaluate the difference between

the quasi-invariants we extracted from. 90% of

configurations show (see Figure 7) a quasi invariant

distance less than: (

(

)

°=θ

61,18;23,0ln

)

Figure 7: Similarity of quasi-invariants.

6 EXPERIMENTATION

Experiments are done on two known databases

(Mokhtarian et al, 1996; Leibe and Schiele, 2003).

First we apply the smoothing process on the

outline shapes (Aouat and Larabi, 2010), then we

apply the part based method to obtain their textual

descriptors (Larabi et al, 2003). The second step is to

perform the indexing process which leads to

determine many classes; all objects of the same class

have the same index.

The first similarity measure is computed for each

model of each class (see examples in Figures 8 and

9). “Dif” is the difference of areas between the

model and the query. (Dif = |the area of the model-

the area of the query |). The symbol “R” means that

the model is recognized, so it verifies, also, the

second similarity measure. In case of many

recognized models, we sort them following parts

areas, in order to find the best model for the query.

Figure 8: Recognition of a car (from Leibe and Schiele

database).

ACCURATE SIMILARITY MEASURES FOR SILHOUETTES RECOGNITION

399

Figure 9: Second example in Mokhtarian database for the

recognition process.

7 CONCLUSIONS

In this paper, we proposed a new method for

silhouettes recognition. Textual description,

smoothing and indexing were previously performed

(Larabi et al, 2003; Aouat and Larabi, 2010; Aouat

and Larabi, 2009).

We have seen the importance of applying

efficient similarity measures to achieve the

recognition process.

Two similarity measures have been proposed:

- The use of parts areas: indeed when two

objects are almost similar, the difference

between their areas is close to zero. The use

of this measure is not sufficient because

different parts may have the same area.

- The computation of geometric quasi-

invariants in order to efficiently compare the

query silhouettes geometry with the models

geometry.

Conducted experiments, performed on two

known databases, showed the method efficiency

and its usefulness to resolve the problem of the

recognition process.

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