JanKees van der Poel
Instituto de Educac¸
ao Superior da Para
ıba – IESP
ao Pessoa – Para
ıba – Brazil
Leonardo Vidal Batista, Carlos Wilson Dantas de Almeida
Departamento de Inform
atica – Universidade Federal da Para
ao Pessoa – Para
ıba – Brazil
Curvature Scale Space, CBIR, correlation coefficient, resampling, resizing, shape classification, full curvature
This work presents a new multiscale, curvature-based shape representation technique for planar curves. One
limitation of the well-known Curvature Scale Space (CSS) method is that it uses only curvature zero-crossings
to characterize shapes and thus there is no CSS descriptor for convex shapes. The proposed method, on the
other hand, uses bidimentionalunidimentionalbidimentional transformations together with resampling
techniques to retain the full curvature information for shape characterization. It also employs the correlation
coefficient as a measure of similarity. In the evaluation tests, the proposed method achieved a high correct
classification rate (CCR), even when the shapes were severely corrupted by noise. Results clearly showed that
the proposed method is more robust to noise than CSS.
Since the beginning of the 90s there has been an
increased research activity in the area of Content
Based Image Retrieval (CBIR). Not only large re-
search teams, such as IBM with the QBIC project, but
also small project groups in the academic and industry
worlds have devoted themselves to this task.
Image retrieval systems are supposed to retrieve
images in an effective manner based on a user’s input
query. This work aims to investigate ways of provid-
ing fast, easy and reliable access to images in elec-
tronic databases. It also intends to create a classifi-
cation and retrieval system that will help to browse,
search, classify and retrieve images in large digitized
Image similarity is very subjective and relative to
each person actual needs: the more a person encoun-
ters an object, the more detailed and differently he or
she can describe it.
There are several simple image retrieval solutions
to the query problem. One of them is to annotate
images with text and then use a traditional textbased
search and retrieval. While fast, this is not effec-
tive when dealing with large collections of complex
images: variability of interpretation is enormous and
also is the human effort required for database anno-
tation. Effective image retrieval systems should ex-
ploit image attributes such as color distribution, mo-
tion, shape (Niblack et al., 1993), structure and tex-
ture (Batista and Meira, 2004).
Image retrieval is based on an ordering of match
scores obtained by searching through a database. The
key challenges in building a retrieval system are the
choice of attributes, their representations, query spec-
ification methods, match metrics and indexing strate-
Shape matching performs an important issue in im-
age retrieval by recognizing and classifying the im-
ages shapes. Some contour shape representations in-
clude eccentricity, circularity (Niblack et al., 1993),
chain code (Freeman and Saaghri, 1978), centroid
distance, cumulative angles (Davies, 1997), Fourier
descriptors, Wavelet descriptors (Zahn and Roskies,
1972; Persoon and Fu, 1977; Kauppinen et al., 1995;
Tieng and Boles, 1997; Yang et al., 1998; Loncaric,
1998) and Curvature Scale Space (CSS) descrip-
tors (Mokhtarian and Mackworth, 1992; Mokhtarian,
1995; Mokhtarian et al., 1996b; Abbasi et al., 2000).
It is generally accepted that CSS descriptors
achieve a good compromise between representation
power and computational efficiency (Dudek and Tsot-
van der Poel J., Vidal Batista L. and Wilson Dantas de Almeida C. (2006).
In Proceedings of the First International Conference on Computer Vision Theory and Applications, pages 401-406
DOI: 10.5220/0001372304010406
sos, 1997; Daoudi and Matusiak, 2000; Mokhtarian
et al., 1996a). The curvature of a planar curve has
perceptual characteristics that have proven to be use-
ful for shape recognition (Pomerantz et al., 1977),
being one of the most powerful tools for representa-
tion, interpretation and recognition of objects in an
image (Mokhtarian and Mackworth, 1992; Pavlidis,
1980; Mokhtarian and Mackworth, 1986; Dudek and
Tsotsos, 1997)). Such characteristics made CSS to be
selected as one of the MPEG-7 contour shape descrip-
tors (Mokhtarian and Bober, 1998).
This paper presents a new method for shape charac-
terization suitable to be used as a retrieval tool in large
image collections. This method is based on the clas-
sical CSS method but but all the available curvature
information is used to perform shape matching, in-
stead of using only the curvature zero-crossing points.
It also uses the correlation coefficient as a measure
of similarity between shapes, allowing a high correct
classification rate, even when the shapes are severely
corrupted by uniform random noise.
The rest of the paper is organized as follows: Sec-
tion 2 describes and discusses the classical CSS de-
scriptor; Section 3 describes the proposed method
and compares it with the classical CSS method; Sec-
tion 4 shows qualitative results of retrieval tests ob-
tained from direct comparison between the classical
CSS method and the proposed method; and Section 5
presents a discussion of the results and the concluding
The classical Curvature Scale Space method for con-
tour representation captures, describes and compares
characteristic shape features of objects based on their
closed contours. It is a multiscale representation of
the inflexion points of a closed contour (Mokhtarian
and Mackworth, 1992), is considered a reliable and
very fast method to perform shape analysis in large
databases and has a number of important properties,
such as:
1. It captures the main features of a shape, enabling
similarity-based retrieval;
2. It reflects properties of the human visual system
perception and offers good generalization;
3. It is robust to non-rigid motion, partial occlusion of
the shape, noise and changes in scale and orienta-
4. It is robust to perspective transformations that re-
sult from common changes of camera parameters
in images and video; and
5. It is compact, reliable and fast.
The idea behind the classical CSS is that a contour
can be represented by its curvature values. It is pos-
sible to compute the curvature at each contour point
based on its neighboring points (Haralik and Shapiro,
1992). The classical CSS takes into account only
those points where the curvature goes from a posi-
tive to a negative value, or vice-versa (curvature zero-
crossings), as illustrated in Figure 1.
Figure 1: Curvature zero-crossings.
To compute the classical CSS representation of a
given object, its contour Γ is initially obtained and
parametrized as in Equation 1.
Γ(u)={(x(u),y(u)) |u [0, 1]} (1)
where u is the normalized arc length parameter, vary-
ing between 0 and 1, and (x(u),y(u)) are parametric
coordinates sampled from the contour at equidistant
values of u, starting at an arbitrary contour point and
following in counterclockwise direction.
Convolving the parametric coordinates of Γ with
a progressively higher standard deviation σ 1-
D Gaussian kernel generates the evolved version
(Mokhtarian and Mackworth, 1992) of Γ, defined
as in Equation 2.
(u, σ)=(X(u, σ),Y(u, σ)) (2)
where X(u, σ)=x(u) g(u, σ), Y (u, σ)=y(u)
g(u, σ),“ is the convolution operator and g(u, σ) is
a Gaussian with standard deviation σ.
The curvature k(u, σ) of Γ
is given by Equa-
tion 3 (Mokhtarian and Mackworth, 1992):
κ(u, σ)=
(u, σ) · Y
(u, σ) X
(u, σ) · Y
(u, σ)
(u, σ)
+ Y
(u, σ)
where X
(u, σ)=x(u) g
(u, σ), Y
(u, σ)=
y(u) g
(u, σ), X
(u, σ)=x(u) g
(u, σ) and
(u, σ)=y(u) g
(u, σ).
After each convolution step, the curvature zero-
crossings of k(u, σ) are located by computing the
curvature for all contour points with Equation 3 us-
ing progressively higher values of σ and determining
where the curvature goes from a positive to a negative
value, and vice-versa. This is done until the curve Γ
becomes completely convex.
Finally, the CSS Image of Γ is a binary image de-
fined by the zero-crossing points of k(u, σ), with u
values in the horizontal axis and σ values in the verti-
cal axis.
As each convolution step smooths the shape con-
tour, the zero-crossings will group two by two, ap-
proach each other, merge and finally disappear, form-
ing what is called a CSS peak. Each zero-crossing
does not necessarily group with an adjacent zero-
crossing: at the end smaller peaks can exist inside
larger ones, due to contour sections delimited by two
zero-crossings that are close together.
To perform a CSS shape-based retrieval, the sim-
ilarity between two shapes is measured by the sum
of the peak differences between all the matched
peaks and the peak values of all the unmatched
peaks (Mokhtarian, 1995; Mokhtarian et al., 1996a;
Mokhtarian et al., 1996b; Abbasi et al., 2000).
Below there is a summary of the steps performed
when using the classical CSS method:
1. Image segmentation;
2. Contour extraction;
3. Shape scale normalization, done by sampling the
shape boundary into a fixed number of points to al-
low matching shapes with different boundary sizes;
4. Shape curvature computation;
5. CSS Image computation; and
6. Shape matching.
Matching CSS Images is difficult because they usu-
ally have a different number of CSS peaks, these
peaks are usually not matching and also can be or-
dered in a quite different way. Mirrored and flipped
shapes need to be considered separately too.
In addition, the classical CSS method only captures
local shape features, missing the global ones (which
are important to shape representation too). To over-
come this, global features such as eccentricity, circu-
larity and number of CSS peaks should be combined
in order to correctly describe the shapes (Zhang and
Lu, 2001).
Due to the dependence on curvature zero crossings,
convex objects may not be well represented with the
classical CSS method. This means that shapes like
circles, ellipsis or convex polygons may not be recog-
nized using this method.
As a final drawback of the classical CSS method,
the boundary sampling and the thresholding processes
done when extracting the CSS peaks causes the CSS
Image to not reflect the true number of convex (or
concave) segments on the shape boundary.
Considering all the classical CSS method problems, a
new approach to retrieve an image based on its con-
tour will now be described.
The proposed method basically performs the same
computations of the classical CSS method. The main
differences are:
1. Its unnecessary to perform the CSS Image compu-
tation step;
2. Full curvature information usage (and not only the
zero-crossing information); and
3. The shape matching step, which uses a different ap-
The proposed method matches shapes using a Full
CSS matrix. This matrix has all the curvature values
computed from Equation 3 with progressively higher
values of σ.
To perform shape matching, the CSS matrices of
the shapes under analysis are computed and com-
pared using the 2-D correlation coefficient r, shown
in Equation 4.
r =
where A, B are the CSS matrices of shapes A and B
B their means, respectively.
As the classical CSS method, the proposed method
suffers from the problem related to the the contour
following arbitrary starting point. To solve this, a one
column rotation is performed to the matrix belonging
to the original shape (the one that is being compared
to the other shapes in the database) each time the cor-
relation coefficient between them is computed.
If one shape has deeper concavities than other, the
σ value used to smooth them completely can be differ-
ent, leading to curvature matrices with non-matching
heights. In this case, directly computing r with Equa-
tion 4 will not be possible. To overcome this, the cur-
vature matrix with the smaller number of lines is re-
sampled to the same number of lines of the higher
curvature matrix.
For noise contaminated shapes, initially the pro-
posed method has results that are worse than those
achieved by the classical CSS method: as the pro-
posed method takes into account all the curvature in-
formation, and as the first lines of the Full CSS matrix
Figure 2: Fish kk4 and its noise contaminated versions (noise ranges of [3, 3], [6, 6], [9, 9] and [12, 12], respectively,
from column two to five).
are those corresponding to the contour without being
smoothed enough, this leads to wrong classifications
results. To solve this problem, the shape smoothing
process of the proposed method can be started with
a higher σ value, generating a new Full CSS matrix,
which then will be used to perform the comparison
Having computed all the correlation coefficients
between the two curvature matrices, one for each ro-
tation, the highest coefficient among all is chosen to
be the similarity measure between the two shapes.
The higher this coefficient is, the more similar are the
This procedure has the advantage of keeping the
information related to the curvatures of the shapes,
allowing for a more precise matching between them.
In this section, a comparison between the classical
CSS method and the proposed Full CSS method in
terms of retrieval results is done.
For sake of comparison, tests were made with two
initial σ values (σ =1and σ =10) when computing
the curvature matrices at the classification stage.
To test the retrieval performance of the classical
CSS and the proposed FCSS method, a Matlab
based indexing and retrieval framework was imple-
mented on Microsoft
XP Professional
running on a PC Athlon64 platform.
For the tests, a small database set, comprising the
first one hundred fish contours (from kk1 to kk100)
from the fish contours database available at (Abbasi
et al., 2005), was selected. The classical CSS method
was implemented using the same matching algorithm
described in (Mokhtarian and Abbasi, 2002).
Classification accuracy was measured by the Cor-
rect Classification Rate (CCR), as in Equation 5:
CF =
× 100% (5)
where c is the number of correctly classified contours,
and t is the number of classified contours.
Each contour was compared to itself and to all oth-
ers belonging to the test database. To test the ro-
bustness of the proposed methods under noisy con-
ditions, uniform random noise in the ranges [3, 3],
0 [−3,3] [−6,6] [−9,9] [−12,12]
Range of uniform noise added to contours
CCRs (%)
Correct Classification Rate achieved by CSS, FCSS
and FCSS
Classical CSS
Full CSS with σ=1
Full CSS with σ=10
Figure 3: CCRs achieved by CSS, FCSS
[6, 6], [9, 9] and [12, 12] was added to each con-
tour. Again, each contour was compared to all noise
contaminated contours of the test database. Figure 2
shows one of the contours (and its noise contaminated
versions) used to perform the comparison tests be-
tween the methods discussed in this work.
Table 1 and Figure 3 both summarize the test re-
sults for the classical CSS method along with the
results for FCSS
and FCSS
, presenting the
CCRs achieved by each method versus the range of
uniform noise added to the shapes.
Figure 4 presents the retrieval results achieved by
FCSS with σ =10in a shape similarity query using
the fish contour kk2. This test was done to visually
assess the accuracy of the proposed method: the sys-
Table 1: CCRs achieved by the classical CSS method,
and FCSS
for the test shapes.
Amplitude CCR (%)
of the random Classical FCSS FCSS
uniform noise CSS method σ =1 σ =10
0 (no noise) 100 100 100
[3, 3] 94 89 99
[6, 6] 91 81 98
[9, 9] 80 65 98
[12, 12] 67 57 95
Figure 4: Similarity retrieval test results, ordered from the
most similar to the less similar according to the system an-
swer: (a) shape used as query (kk2); (b) kk2; (c) kk13; (d)
kk31; (e) kk22; and (f) kk20.
tem was set to return the five more similar shapes to
the one chosen. The ve fishes returned were kk2 it-
self, kk13, kk31, kk22 and kk20, ordered by similarity
according to the system answer.
The time spent by the proposed method to retrieve
one shape from the database was about 19 seconds.
This means that, given one shape, the system spent
19 seconds to retrieve 100 other shapes and return the
correct (or incorrect) shape matching the given one.
The classical CSS method spent 15 seconds to per-
form the same retrieval task.
The memory needed for each Full CSS matrix is
the same as for an image of size about 300×200. The
implementation used in this work stored the
FCSS data as an array of 16 bit-unsigned integers,
meaning that one FCSS matrix has about 480 K bytes.
This memory amount can be reduced by using an ar-
ray of 8 bit-unsigned integers.
This paper proposed a new, simple and highly ac-
curate shape classification scheme based on the well
known CSS method. The main innovations of the new
representation scheme over the classical CSS method
are the use of all curvature information available, of
different initial σ values to improve the retrieval per-
formance and of the correlation factor as a similarity
It is worth to say that in (Junior and da Costa,
1998), a similar multiscale, curvature-based shape
representation method was shown, but the author only
describes his technique and does not show any results
regarding its shape retrieval performance. Besides
that, his method uses Fourier Transforms and is not
directly related to the CSS method.
To assess the performance of the classical CSS and
the FCSS method, the test shapes were contaminated
with random uniform noise ranging from low to high
amplitudes and a database shape retrieval was done,
as described in Section 4.
Evaluating the effects of adding noise to the test
shapes over classification accuracy, as in Figure 3,
showed that the performance of the classical CSS
method quickly degrades. This is due to the fact
that when noise range goes beyond [6, 6], important
regions of the contour will overlap (as can be seen
in Figure 2). In contrast, when using σ =10the
proposed classifier maintains its performance even in
presence of severe noise, as can be seen in Figure 3.
Table 1 and Figure 3 together show that the FCSS
method with σ =10achieved CCR = 95% with noise
amplitudes up to [12, 12], while the classical CSS
method achieved only CCR = 67% under the same
The robustness of the proposed method under noisy
conditions should be pointed: a retrieval for similar
shapes showed very good results, as can be seen from
Figure 4.
Table 1 shows that simply increasing the σ initial
value also increased the classifier performance: for
a noise with amplitude range [12, 12], the classical
CSS method achieved CCR = 67% while the FCSS
method with σ =10achieved CCR = 95% (a much
better result than the FCSS method with σ =1, which
only achieved CCR = 57%).
The time spent in a simple query by the proposed
method is still high. This is due to the fact that all the
test platform was implemented using interpreted code
in Matlab
without any speed optimization. The au-
thors are now implementing the same test framework
in Java, seeking for a more efficient retrieval.
It is clear that the proposed method consistently
outperforms the classical CSS method. This superior-
ity is still more remarkable when shapes are severely
contaminated by noise and shows that the proposed
method is suitable to be used in such conditions.
Other research directions include more tests to as-
sess the classification and retrieval results under dif-
ferent types of noise; investigate the performance
of the FCSS method in other domains, such as tu-
mor classification and recognition (de Almeida et al.,
2005), and in shapes with large boundary indentations
and protrusions; and investigate the use of dictionary
created by lossless data compression algorithms, such
as LZW or PPM, instead of the correlation coefficient
as the similarity measure (Batista and Meira, 2004).
The authors wish to thank Professor Fernando Manuel
Bernardo Pereira, from Instituto Superior T
Lisboa, for his valuable contribution to our Image
Processing Group, and Professor Farzin Mokhtarian
for his fish contour database.
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