Journal of Software Engineering and Applications, 2011, 4, 371-378
doi:10.4236/jsea.2011.46042 Published Online June 2011 (http://www.SciRP.org/journal/jsea)
371
Analysis of the Relevance of Evaluation Criteria
for Multicomponent Image Segmentation
Sié Ouattara1, Georges Laussane Loum1, Alain Clément2, Bertrant Vigouroux2
1Laboratoire d’Instrumentation, d’Image et de Spectroscopie (L2IS), Institut National Polytechnique Félix Houphouët-Boigny
(INPHB)/DFR-GEE, Yamoussoukro, Côte d’Ivoire; 2Laboratoire d’Ingénierie des Systèmes Automatisés (LISA), Institut Univer-
sitaire de Technologie, Angers, France.
Received May 8th, 2011; revised June 2nd, 2011; accepted June 11th, 2011.
ABSTRACT
Image segmentation is an impo rtant stage in many applications such as image, video and computer processing. Gener-
ally image interpretation depends on it. The materials and methods used to demonstra te are described. The results are
presented and analyzed. Several approaches and algorithms for image segmentation have been developed, but it is dif-
ficult to evaluate the efficiency and to make an objective comparison of different segmentation methods. This general
problem has been addressed for the evaluation of a segmentation result and the results are available in the literature.
In this work, we first presented some criteria of evaluation of segmentation commonly used in image processing with
reviews of their models. Then multicomponent synthetic images of known composition are applied to these criteria to
explore the operation and evaluate its relevance. The results show tha t choosing an assessment method depends on the
purpose, however the criterion of Zeboudj appears powerful for the evaluation of region segmentations for properly
separated classes, on the contrary the criteria of Levine-Nazif and Borsotti are adap ted to the methods of classification
and permit to build homogeneous regions or classes. The values of the Rosenbeger criterion are generally low and
similar, so hard to make a comparison o f segmentations with this criterion.
Keywords: Quality of Segmentation, Multicomponent Images, Supervised and Unsupervi sed Eval u ati on ,
Synthetic Images, Metric
1. Introduction
Segmentation is an essential step in image processing
to the extent that it affects the interpretation which will
be made of these images in many application areas
[1-4]. They are based on different approaches, such as
contour, region and texture. Many algorithms have
been proposed in recent decades. Given the multitude
of proposed methods, the problem of assessing the
quality of segmentation becomes paramount.
Originally, the first criteria for evaluating the quality
of segmentation were purely subjective: the observer
merely to examine different results of segmentation, to
decide which the best was according to the objective. It
soon becomes necessary to replace this qualitative
method by quantitative methods, defining appropriate
quality criteria. The first quantitative criteria date from
the Nineties (90), but the field remains open, and new
criteria appear regularly in literature [5-7].
These criteria are not intended to provide the abso-
lute quality of a segmentation: they serve just to com-
pare, using a given criterion, different segmentation
algorithms applied to the same image, or to set up an
algorithm to adjust its parameters to provide the best
result.
It should be noted that classification with a particular
criterion, different algorithms of segmentation can be
changed if we change the criterion. Similarly, a choice
of parameters optimizes a segmentation algorithm, with
respect to a given criterion it may be changed if we
change the evaluation criterion.
Throughout this paper, the image segment will be
denoted I. After segmentation, we get an image
s
I
,
formed with
s
N regions , where
i
S{1, ,}
s
iN ,
checking the properties:
1
s
ij
N
i
SS
SI









 (1)

Analysis of the Relevance of Evaluation Criteria for Multicomponent Image Segmentation
372
Denoting by A the number of pixels in the image and
by Ai that of the region , properties 1 can be written:
i
S

1
s
N
i
A
Card IS
 (2)
One generally agrees to classify the methods of as-
sessing the quality of a segmentation in two categories,
corresponding respectively to a supervised evaluation
and an unsupervised evaluation [6,8].
2. Criteria for Evaluating the Region
Segmentation
2.1. Supervised Evaluation
The assessment is known as supervised when a reference
segmentation v
I
(also called ground-truth) is defined.
This one can be established on a natural image, by one
(or more) operator human expert of application domain,
using drawing software. A more comfortable case is that
of the synthetic images whose ground truth is rigorously
accessible.
The evaluation of a segmentation algorithm is then
performed by comparing the segmented image
s
I
with
the ground-truth v
I
. Denoted by j, where,
the v regions of the reference image. The question
which is asked is that of the measurement of the similar-
ity (or dissimilarity) between the reference segmentation
and the algorithmic segmentation.
V{1 }
v
, ,jN
N
One possible answer is provided by the method of Vi-
net, search recursively the pairs of regions with
the highest recovery [9]. recovery regions and
(, )
ij
SV
i
S
ij
T
j
V is defined by:

iji j
TCardSV


(3)
It makes it possible to build a table of covering

,
s
v
TII
t
, whose elements are the ij . One initially se-
lects in the table the cell corresponding to the maximum
ij . The two corresponding regions are then paired. Then
one removes in the table the corresponding line and
column, and we iterate the operation until all the cells are
treated. K couples thus are obtained:
t


min ,
s
v
K
NN (4)
Each couple presents a covering k, where t{1,, }kK

 .
The measurement of Vinet is then defined by:

1
1
,1
K
s
v
k
VIN IIt
A
 k (5)
Assuming a perfect recovery, (1) and (5) show that
Vinet’s criterion takes the value 0. It tends to 0.5 for
minimal recoveries. The method iteratively chosen to
match regions is suboptimal; it does not guarantee
maximum recovery across all regions.
Other supervised evaluation criteria can be defined [8],
taking into account the number and position of the evil
segmented pixels, or even their color. They will not be
used in this article.
2.2. Unsupervised Evaluation
In most cases, we do not have a ground-truth. It is thus
necessary to develop calculable evaluation criteria only
on the image
s
I
, segmented by algorithm. Many criteria,
more or less discriminating, have been proposed. They
are based on inter-region variability and (or) intra-region
uniformity.
Variability or uniformity is measured from the colors
of pixels in the image. The color of the pixel p will be
denoted


Cp, and the average color of a region R of
the image will be denoted

CR. In the particular case
of textured images, texture attributes may also be imple-
mented. They will form the vectors that we denote


GRwhen characterized in a region R of the image.
2.2.1. Intra-Region Uniformity Criterion of Levine
and Nazif
The intra-region uniformity is translated here by the
normalized variance of colors inside each region [10].
The colors’ average of the region is written:
i
S
 
1
i
ipS
i
CS Cp
A
 (6)
The normalized color variance of the component,
on the region , is expressed:
q
C
i
S

 

 

22
2
2
1
4
max min
i
ii
qqi
pS
i
qi
pS qpSq
CpCS
A
SCp Cp 





 




(7)
where q C denotes the q-th component of C. The total
variance of the color on the region is written:
i
S
 
22
1
n
iq
q
S 

i S (8)
Assuming an image with n components.
The criterion of Levine and Nazif is defined by:
 
2
1
1
s
N
s
i
i
LEV IS 


 (9)
Assuming that all regions are perfectly homogeneous,
the test is 1 since the variance of each region (the nu-
merator of the fraction in the (7)) is zero. The criterion
decreases in presence of inhomogeneity. An alternative is
to weight in the sum on i, each region by the number of
pixels.

Analysis of the Relevance of Evaluation Criteria for Multicomponent Image Segmentation373
2.2.2. Dissimil ari t y Meas ure of Liu and Yang
Let us consider i the sum of Euclidean distances (dist)
between the colors of pixels in the region Si and the av-
erage color of :
e
i
S


,
i
ii
pS
edistCpCS





(10)
The criterion of Liu and Yang is defined by [11]:

2
1
1
1000
sNi
ss
ii
e
LIUIN
A
A

 (11)
If all regions are perfectly homogeneous, the criterion
is 0 because of i. Contrary to Levine and Nazif’s crite-
rion, that of Liu and Yang does not just evaluate in-
tra-region variance: it penalizes the over-segmentation by
the presence of many regions in numerator and the area
of regions in denominator.
e
2.2.3. Criterion of Borsotti
The criterion of Liu and Yang strives only partially
against the over-segmentation. Suppose that it leads to a
large number of small regions, all homogeneous: the
presence of the factor i in the (11) gives then
, which is characteristic of a “good” seg-
mentation, this is in contradiction with the decision of
over-segmentation as starting hypothesis.
e

0
s
LIUI
To overcome this drawback, Borsotti proposed a
neighboring criterion, penalizing small regions even in
the case where they are homogeneous [12]



2
2
2
1
1
10001 log
s
Ni
i
ss
iii
A
e
BOR IN
AA
A











(12)
where

i
A
 is the number of regions comprising Ai
pixels. The first term under the summation sign penalizes
large inhomogeneous regions, while the second penalizes
small regions of the same size, even if they are homoge-
neous. A “successful” segmentation will be characterized
by the criterion of Borsotti close to 0.
2.2.4. Inter-Region and Intra-Region Contrast of
Zeboudj
The above criteria are only interested in the intra-region
homogeneity. The criterion of Zeboudj takes into account
not only the intra-region homogeneity, but also the in-
ter-region contrast, in a neighborhood of the
pixel p [13] .

Wp
The contrast between two pixels p and s of
an image is proportional to the distance separating the
colors of these pixels:

,ps

  
max
,
,dist CpC s ps d




 (13)
where dmax is the maximum distance possible in the mul-
ticomponent space used.
The contrast


I
i
S within the region i, and the
contrast
S


E
i between the region Si and the
neighboring regions are respectively defined by:
S
  
1max, ,
i
I
ii
pS
j
SpssW
A
 pS




 (14)
  
1max,,,
i
E
ii
pF
i
SpssWp
L
 
i
SsS





(15)
where i is the length of the boundary i L
F
delimiting
the region i. The global contrast of the region
is defined by:
S

i
S

i
S



  

10
0
0elseif
Ii
I
iEi
Ei
iEi Ii
SifS S
S
SSifS





 





(16)
Zeboudj’s criterion is deduced by:
 
1
1s
N
s
i
ii
Z
EB IAS
A

 (17)
This criterion increases with the quality of segmenta-
tion. It is not suitable for images too noisy or textured.
2.2.5. Criter ion of Rosenberger
To take into account the possible presence of textured
regions in the segmented image, while addressing the
inter-region disparity, Rosenberger offers a different
treatment of textured regions and non-textured regions in
the defining of the evaluation criterion of the segmenta-
tion [14]. The textured character or not of a region is
established using the co-occurrence matrices (thus per-
forming the pre-processing of multicomponent images
into scalar images, which is simplified by a process of
multiple thresholding in order to reduce the size of
co-occurrence matrices). The non-textured regions are
characterized by their colors , and textured
regions by a vector of 29 texture attributes, noted G,
chosen, because of their discriminating power among the
classic attributes of co-occurrence, lengths of intervals,
and local histograms of local extremas.

i
Cp S

 Intra-region disparity
The disparity of non-textured regions is characterized by
the intra-region variance of pixel colors in a manner
analogous to that used by Levine and Nazif. In the region
Si attributed the disparity coefficient:

Analysis of the Relevance of Evaluation Criteria for Multicomponent Image Segmentation
374
i
 
i
DS S   (18) given by:
 
1
1s Ni
E
s
i
s
A
DI DS
NA


calculated using Equations (6) to (8). Ei
(24)
For the textured regions, the attributes used are not any
more the colors, but the vectors of texture . Their
calculation of the coefficient of disparity

i
GS


I
i
DS as-
sociated with textured regions is more complex, and will
not be detailed here, because all the images used in the
continuation of this work will be considered non-textured.
The interested reader may however see reference [14].
 Criterion of Rosenberger
Finally, the criterion of Rosenberger is defined by:
  
1
2
I
sE
s
DI DI
ROS I s (25)
The global intra-region disparity is given by: This criterion decreases when the segmentation quality
increases. A sub-segmentation is penalized through an
intra-region disparity
I
D strong, and over-segmentation
will be through an inter-region disparity
E
D low.
 
1
1s
Ni
I
s
i
s
A
DI DS
NA

Ii (19)
3. Analysis of Unsupervised Evaluation
Criteria, Results and Discussion
 Inter-region disparity
Between two non-textured regions, the disparity is pro-
portional to the distance separating the average colors of
the two regions: The behavior of the above criteria will be studied using
synthetic images constituted of regions of uniform color,
perfectly controlled: their segmentation in region is thus
known. The segmented image and the ground-truth being
rigorously similar, it is unnecessary to examine the be-
havior of Vinet’s criterion, which will systematically
give a result equal to 0 (perfect overlap). Only then we
will study the unsupervised evaluation criteria (except
that of Liu and Yang: we have preferred to him that of
Borsotti, which is an improvement). The window W used
to calculate Zeboudj’s criterion here is a window of size
3 × 3 (neighboring order 8). To calculate Rosenberger’s
criterion, all regions will be considered non-textured.

 
max
,
,ij
ij
dist C SC S
DSS d




 (20)
where dmax is the maximum distance possible in the mul-
ticomponent space used.
Between two textured regions, disparity takes into ac-
count the textural distance vectors, and their norm.

 


,
,ij
ij
ij
dGS GS
DSS GS GS


 (21)
3.1. Characteristics of Synthetic Images Used
Between two regions one of which is textured and the
other not, the disparity is set to: The test images are 4 synthetic images shown in Figure
1 and whose detailed composition is described in Table 1 .
Their segmentation (shown in false color to better high-
light the regions) is shown in Figure 2.

,
ij
DSS1 (22)
If we denote 1i
iiq
the set of i neighboring
regions of i. The inter-region disparity of the region
is written:
{,, }SS q
S
i
SThe first two images (Synt1a_Lisa and Synt1b_Lisa)
present two uniform regions, of different sizes. The col-
ors of these regions are clearly separated for the image
Synt1a_Lisa, and otherwise very similar (and indistin-
guishable to the eye) for the image Synt1b_Lisa. The last
two images (Synt2a_Lisa and Synt2b_Lisa) present three


1
1,
qi
i

E
i
ji
i
DS DSS
q
ij (23)
and the global inter-region disparity of the image Is is
Synt1a_Lisa Synt1b_Lisa Synt2a_Lisa Synt2b_Lisa
Figure 1. Synthetic images.

Analysis of the Relevance of Evaluation Criteria for Multicomponent Image Segmentation375
Seg(Synt1a_Lisa) Seg(Synt1b_Lisa) Seg(Synt2a_Lisa) Seg(Synt2b_Lisa)
Figure 2. Result (in arbitrary colors) of the segmentation.
Table 1. Building of synthetic images of Figure 1.
(a)
Building of synthetic images
Synt1a_Lisa Synt1b_Lisa
R G B Population R V B Population
51 0 204 51200 203 101 0 14336
204 102 0 14336 204 102 0 51200
(b)
uniform regions.
On the Synt2a_Lisa image, two regions have neigh-
boring colors (and indistinguishable with the eye) and
Different sizes, higher than that of the third region, from
which the color is distant. On the Synt2b_Lisa image,
two regions are identical in size, equal to half of that of
the third region: the colors of the two regions of identical
size are very close one to the other (indiscernible to the
eye), and far away from the color of the third.
3.2. Calculation and Analysis of Criteria
Evaluation for Segmentation
The evaluation criteria for unsupervised segmentation,
computed for these images, take the values reported in
Table 2.
Each region is of uniform color, Levine’s criterion re-
turns the possible maximum value 1, as expected.
For the same reason, Borsotti’s test is sensitive only to
the size of regions and the number of regions with the
same size (second term under the summation sign in
(12)). Segmentation provides a partition exactly the same
for the first two images, and consequently, the criteria of
Borsotti are identical in both cases. Compared to the first
two images, the latter two are penalized by the criterion
of Borsotti (which increases), because the number of
regions increases from 2 to 3. The fourth image is most
penalized than the third because it has two regions of
identical size (parameter ν of Borsotti’s criterion).
Table 2. Value of evaluation criteria for unsupervised seg-
mentation for synthetic images of Figure 1.
Criterion
Image Levine
and
Nazif
Borsotti Zeboudj Rosenberger
Synt1a_Lisa1 1,13.10–16 0,6000 0,3500
Synt1b_Lisa1 1,13.10–16 0,0026 0,4993
Synt2a_Lisa1 2,17.10–16 0,1957 0,4584
Synt2b_Lisa1 8,12.10–16 0,6753 0,3873
Building of synthetic images
Synt2a_Lisa Synt2b_Lisa
R G B Population R V B
Population
21 250 0 21200 20 20 20 16384
23 250 0 30000 22 20 20 16384
51 50 54 14336 250 250 250 32768
As each region is uniform in color, the internal con-
trast of regions
I

is zero, and Zeboudj criterion no
longer considers the contrast between a region and its
neighbors. It penalizes the image Synt1b_Lisa (ZEB =
0.0026) compared to the image Synt1a_Lisa (ZEB =
0.6000). The same reasoning, with the same conclusions
can be made with the criterion of Rosenberger.
3.3. Influence of Inter-Class Colorimetric
Distance and the Popul ation of Regions
Consider a square image of a hand consisting of two
homogeneous regions of color respective C1 and C2
which n components are coded from levels 0 to 21
q

.
The position of the boundary between the two regions is
marked by a variable x (
Figure 3) proportional to the
population of both regions.
We find generalize the model of images Synt1a_Lisa
and Synt1b_Lisa of Figure 1. The calculation of the
evaluation criteria for segmentation provides here the
following results:
1LEV  (26)

62 2
6
21 1
2 1000 1
32 21
2 1000
if x
ax x
BOR
if x
a

1

 







(27)

12
max
,
1dist CC
ZEB ad  (28)

Analysis of the Relevance of Evaluation Criteria for Multicomponent Image Segmentation
376
Figure 3. Square image consisting of two regions of color
C1 and C2.


12
max
,
2
8
dist CC
d
ROS

 (29)
The Equation (26) shows that Levine’s criterion values
the segmentation into homogeneous regions, regardless
of their sizes and colors. Segmented into two neighboring
regions of nearly identical color will be as good as if the
colors were distant, which may be irrelevant for the in-
tended application.
The function between brackets in (27) is decreasing in
the interval [0, 0.5] and increasing in the interval [0.5, 1].
This shows that Borsotti’s criterion values the segmen-
tation in homogeneous regions of similar size, regardless
of their spacing colors. A segmentation into two neigh-
boring regions of very different sizes will be considered
bad, even if the application is to detect a small homoge-
neous region within a greater one.
Equations (28) and (29) show that Zeboudj’s and
Rosenberger’s criteria value the segmentations into two
neighboring homogeneous regions in proportion to their
color difference, and this result holds true regardless of
the sizes of the two regions.
3.4. Influence of the Metric on Zeboudj’s and
Rosenberger’s Criteria
Denote ZEBmin and ZEBmax (respectively ROSmini and ROSmax)
limits of variation of Zeboudj parameter (respectively
that of Rosenberger) for an image which model is that of
Figure 3. The minimum distance between two colors is
equal to 1, whether we use the Euclidean metric, that of
Manhattan, or that of Chebychev. Since the n compo-
nents of the image are each coded on q bits, the maxi-
mum distance between two colors is written:
2
max
2inEuclidianmetric
2 inManhattanmetric
2in Chebychev metric
q
q
q
n
dn








(30)
The range of variation of Zeboudj and Rosenberger
criteria that results is summarized in Table 3, for gray-
scale images (n = 1), color images (n = 3) and multi-
component images (n = 10), the tonal resolution q can
vary from 1 to 8 bits per component. ZEBmax and ROSmini,
who write the best segmentations, are not listed in the
table because they are respectively 1 and 0.125 for all
configurations.
For scalar images (n = 1), the values of ZEBmin and
ROSmax repeated identically whatever the type of metric,
which is not surprising since the distances are dmax iden-
tical.
For all metrics, the value of 2 × ZEBmin characteristic
of bad segmentation is less than 0.1 regardless of the
number of components, provided that the tonal resolution
is greater than or equal to 4 bits. This provides ranges of
variation in a width at least equal to 0.9 (for 4 bits per
pixel), which approaches the limit 1 when the tonal reso-
lution increases. It is therefore possible in this case to use
the metric of choice, without significant impact on the
available scale of classification of segmentation algo-
rithms.
We will have an incentive to choose Chebychev’s
metric, which induces less computation. At lower tonal
resolutions, the range of possible values for 2 × ZEB
shrinks, until a width equal to 0.5 for binary images. But
again this difference remains the same whatever the met-
ric used.
For Chebychev’s metric, the maximum distance be-
tween two colors do not depend on the number of com-
ponents (see (30)). This explains the identical repetition
of values of ZEBmin and ROSmax, whatever the number of
components (two last columns of Table 3).
For all metrics, the value of ROSmax characteristic of
poor segmentation is between 0.240 and 0.250 regardless
of the number of components, as long as the tonal resolu-
tion is greater than 4 bits. This provides ranges of varia-
tion in a width at least equal to 0.115 (for 4 bits per
pixel), which tends to the limit 0.125 when increases
tonal resolution. Again it will be possible to use the met-
ric of choice. At lower tonal resolutions, the range of
possible values for ROS narrows to a width equal to
0.0625 for binary images. But again this difference re-
mains the same whatever the metric used.
4. Conclusions
This work has enabled us to study the unsupervised
evaluation methods of segmentation to understand their
relevance. We showed that their relevance is related to
the metric used, the distance between color regions or
classes, classes or regions size, the tonal resolution of
images and the number of components n of the images
without forgetting the homogeneity of the regions. We

Analysis of the Relevance of Evaluation Criteria for Multicomponent Image Segmentation
377
Table 3. Value of evaluation Variation range of Zeboudj and Rosenberger criteria, for images consistent with the model in
Figure 3 (a/2 was assumed equal to 1 for the calculation of the Zeboudj criterion).
Euclidean distance Manhattan distance Chebychev distance
n q 2*ZEBmin ROSmax 2*ZEBmin ROSmax 2*ZEBmin ROSmax
1 0.500 0.188 0.500 0.188 0.500 0.188
2 0.250 0.219 0.250 0.219 0.250 0.219
3 0.125 0.234 0.125 0.234 0.125 0.23
4 0.063 0.242 0.063 0.242 0.063 0.242
5 0.031 0.246 0.031 0.246 0.031 0.246
6 0.016 0.248 0.016 0.248 0.016 0.248
7 0.008 0.249 0.008 0.249 0.008 0.249
1
8 0.004 0.250 0.004 0.250 0.004 0.250
1 0.289 0.214 0.167 0.229 0.500 0.188
2 0.144 0.232 0.083 0.240 0.250 0.219
3 0.072 0.241 0.042 0.245 0.125 0.234
4 0.036 0.245 0.021 0.247 0.063 0.242
5 0.018 0.248 0.010 0.249 0.031 0.246
6 0.009 0.249 0.005 0.249 0.016 0.248
7 0.005 0.249 0.003 0.250 0.008 0.249
3
8 0.002 0.250 0.001 0.250 0.004 0.250
1 0.158 0.230 0.050 0.244 0.500 0.188
2 0.079 0.240 0.025 0.247 0.250 0.219
3 0.040 0.245 0.013 0.248 0.125 0.234
4 0.020 0.248 0.006 0.249 0.063 0.242
5 0.010 0.249 0.003 0.250 0.031 0.246
6 0.005 0.249 0.002 0.250 0.016 0.248
7 0.002 0.250 0.001 0.250 0.008 0.249
10
8 0.001 0.250 0.000 0.250 0.004 0.250
also showed what ranges of evaluation criteria were good
or bad.
Knowing that the study of the relevance of a segmen-
tation algorithm requires choosing an evaluation criterion
of segmentation, therefore to realize the goal of the seg-
mentation in homogeneous regions and well separated,
we recommend an appropriate combination of Zeboudj’s
and Borsotti’s criteria.
In Perspectives, an experiment with models of syn-
thetic multi-region images will achieve a comprehensive
study of the relevance of unsupervised evaluation meth-
ods of segmentation.
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