Fuzzy Model-based Algorithm for 3-D Bone Tumour Analysis
Joanna Czajkowska
Media Systems Group, Institute for Vision and Graphics, University of Siegen, Hoelderlinstr. 3, Siegen, Germany
Department of Biomedical Engineering, Silesian University of Technology, ul. Akademicka 16, Gliwice, Poland
Keywords:
Model based Analysis, Fuzzy Interference System, Fuzzy Connectedness Analysis, Gaussian Mixture Model.
Abstract:
In this paper, a new fuzzy model based algorithm for 3-D bone tumour segmentation in MR series is intro-
duced. The presented segmentation procedure is based on a modified fuzzy connectedness method. The there
required fuzzy affinity values are estimated using a fuzzy inference system, whose fuzzy membership func-
tions are structured on the basis of gaussian mixture model of analyzed image regions. The 3-D fuzzy tumour
model is generated using different MR modalities acquired during a single examination. The segmentation
abilities of prototype system have been tested on a MR database consisting of 27 examinations composed of
two different sequences each.
1 INTRODUCTION
According to (Davies et al., 2009; Husband and
Reznek, 2004), bone tumour is an abnormal growth of
cells within a single bone, spreading to another one,
muscles or soft tissue in their surroundings. They
are usually found in children and young adults and
their early diagnosis can be crucial for the treatment
applied. The diversity of bone tumours in children
still features many diagnostic and therapeutic prob-
lems. Determination of their nature requires experi-
ence and close collaboration of specialists from vari-
ous areas. Despite the significant progress of imaging
techniques, many cases are diagnosed too late.
The bone tumours diagnostics is mostly based on
Magnetic Resonance (MR) imaging, where during a
single examination, series in different MR modalities
are acquired. However, different tumour types vary in
their appearance even in the same modality. Largely
only the comparative radiological analysis taking into
consideration several acquired series enables a reli-
able diagnosis.
Due to the fact, that bone tumours are quite rare,
the problem of their segmentation is not often dis-
cussed in literature. Varied intensity levels in MR se-
quences constituting different tumours cause the de-
scribed segmentation methods (Ma et al., 2005; Zhao
et al., 2004; Pan and Li, 2003) to be dedicated to
one tumour type only. A wide range of currently
available imaging techniques differentiates the seg-
mentation procedure to dynamic MR based (Zhao
et al., 2004; Zhao et al., 2003) as well as static MR
based (Ma et al., 2005; Pan and Li, 2003) techniques.
All the procedures presented in the mentioned papers
combine the information coming from different MR
modalities. The segmentation algorithm proposed
in (Ma et al., 2005) is based on fuzzy connected-
ness analysis developed by (Rosenfeld, 1979; Udupa
and Samarasekera, 1996) and is commonly used in
different medical applications (Pednekar et al., 2008;
Udupa et al., 2002). The fuzzy connectedness princi-
ples have been tested in dozens of studies in past 15
years.
There exist different fuzzy logic based techniques
dedicated to medical applications described in litera-
ture (Yamaguchi et al., 2010; Hata et al., 2000; Tolias
and Panas, 1998). The fully automated fuzzy topol-
ogy method used for brain image analysis is proposed
in (Mari and Dellepiane, 1996). Brain analysis inves-
tigating its morphological changes based on a combi-
nation of Bayesian classification with Gaussian Mix-
ture Model (GMM) and fuzzy active surface is pre-
sented in (Yamaguchi et al., 2010).
The differences in grey intensity levels building
bone tumours areas depending on their location in
the human body make reliable automatic segmenta-
tion and direct application of mentioned procedures
impossible. Therefore, this paper presents a new
segmentation algorithm combining GMM and fuzzy
inference systems in the fuzzy connectedness pro-
cedure, insensitive to tumour type and location in
the body. The developed 3-D segmentation method,
185
Czajkowska J..
Fuzzy Model-based Algorithm for 3-D Bone Tumour Analysis.
DOI: 10.5220/0004498301850192
In Proceedings of the 5th International Joint Conference on Computational Intelligence (FCTA-2013), pages 185-192
ISBN: 978-989-8565-77-8
Copyright
c
2013 SCITEPRESS (Science and Technology Publications, Lda.)
based on the previously segmented tumour as well as
surrounding tissues regions on a single slice, adopts
the fuzzy inference system parameters to enable the
analysis of the whole study.
Radiological diagnostic of bone tumours relies
on comparative analysis of different MR images ac-
quired during one examination. With this in mind, in
the presented methodology a parallel analysis of two
different MR series is applied.
In the following section, a short introduction to
the fuzzy connectedness-based segmentation proce-
dure is given. In section 3 the membership functions
structured based on GMM are described. Section 4
introduces the used fuzzy inference system and sec-
tion 5 presents the developed algorithm. Discussion
concerning performed experiments and obtained seg-
mentation results is given in section 6. Then, the last
section (section 7) concludes the work and presents
some plans for the future.
2 FUZZY CONNECTEDNESS
BASED SEGMENTATION
The idea of fuzzy connectedness analysis in image
processing and image segmentation has been given
in works (Rosenfeld, 1979; Udupa and Samarasek-
era, 1996). The there presented methodology oper-
ates on multidimensional, multifeature sets of data,
being connected and ordered. The points classified
into an object are strongly connected with some rela-
tions having relatively lower values, when it comes to
points outside the object. In medical image segmen-
tation a multifeature data set often consists of grey
intensity levels of pixels (or voxels in volumetric
data) in acquired CT, MR, US etc. studies. The image
fusion methods applied afterwards make it possible
to simultaneously analyse them all. In the presented
study only MR data of bone tumours are collected,
however the multifeature dataset is constructed with
different MR modalities, namely T2-weighted, T1-
weighted, T1-weighted contrast enhanced, etc.
Then, the segmentation procedure takes into con-
sideration local similarities of the analyzed voxels,
exploring their position e = (e
x
,e
y
,e
z
) and gray in-
tensity levels I
d
(e), where d = {1,...,D} is the di-
mensionality of feature space.
Fuzzy connectedness of two image points is es-
timated on the basis of their fuzzy relation fuzzy
affinity κ
κ = {((e, d),µ
κ
(e,d)) : (e, d) C ×C}, (1)
where µ
κ
[0, 1] is the fuzzy affinity membership
function of spels (spatial elements) e and d. The
reflexive: µ
κ
(e,e) = 1 and symmetric: µ
κ
(e,d) =
µ
κ
(d, e) fuzzy affinity is mostly given as
µ
κ
(e,d) = µ
α
(e,d) ·g(µ
ω
(e,d), µ
ψ
(e,d)), (2)
where µ
α
is the functional form of adjacency rela-
tion α and µ
ω
, µ
ψ
are intensity-based and intensity
gradient-based components of the affinity, respec-
tively. There are different forms of (2) discussed
in (Udupa et al., 2002), from which the most popu-
lar in medical applications is the weighted gaussian
variant
µ
κ
(e,d) = µ
α
· (w
1
H
1
(e,d) + w
2
H
2
(e,d)), (3)
with parameters w
1
and w
2
denoting positive con-
stants fulfilling
w
1
+ w
2
= 1. (4)
Components H
1
and H
2
are defined as:
H
1
(e,d) = exp
1
2σ
2
1
I(e)+I(d)
2
λ
1
2
,
H
2
(e,d) = exp
1
2σ
2
2
(|I(e) I(d)| λ
2
)
2
.
(5)
Pairs λ
1
, σ
1
and λ
2
, σ
2
are the expected parameters
of the segmented object, describing its gray intensity
and gradient.
To determine the relations of spels e and d the
concept of digital path has been introduced (Udupa
and Samarasekera, 1996). A nonempty path p
ed
from
e = e
(1)
to d = e
(m)
is any sequence of elements
e
(1)
,e
(2)
,...,e
(m)
, such that for any i [1, m 1]
pair e
i
,e
(i+1)
a link exists. The strength of a path
is given by the strength of its weakest link (with the
smallest affinity). The strength of the ”strongest”
paths between two image points (spels) e and d de-
scribes their connectedness.
Finally, the fuzzy κ-connectedness relation K be-
tween two image points e and d is given as follows
µ
K
(e,d) = max
p
ed
P
ed
[µ
N
(p
ed
)], (6)
where
µ
N
(p
ed
) = min
i
{µ
κ
(e
(i)
,e
(i+1)
)}. (7)
Fuzzy affinity scene
o
with respect to object’s
starting point o is then given by
o
(e) = µ
K
(o,e). (8)
Then, the segmented fuzzy object O(o) containing
starting point o is obtained using the thresholding pro-
cedure on scene
o
. The problem of threshold se-
lection is solved by introducing the second object,
treated as a background region with its own seed
point b. Therefore, spel e belongs to object O(o) if
µ
K
(o,e) > µ
K
(b,e). The already described approach
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is called the Relative Fuzzy Connectedness method
and it is discussed in detail in (Udupa et al., 2002;
Udupa and Samarasekera, 1996). To solve the short-
est path problem the authors use the dynamic pro-
gramming approach, which in (Carvalho et al., 1999)
has been replaced by the Dijkstra’s Algorithm. In the
later FC applications (Saha and Udupa, 2001) also the
single seed points belonging to the object as well as
the background have been replaced by the seed points
sets.
In cases of clearly visible tissues and sharp enough
edges the already described FC-based segmentation
method yields very good results. Based on the se-
lected seed points areas the required intensity and in-
tensity gradient parameters are there easy to estimate.
The pathologies, like soft tissue tumours, with a more
complex structure can be segmented applying a clus-
tering based FC analysis presented in (Badura et al.,
2011). The analysed image data are first clustered and
the obtained clusters parameters are then utilised in
the FC step.
The idea introduced in this paper is to adopt the
fuzzy connectedness approach to multifeature bone
tumour analysis. The presented methodology is based
on two different MR modalities. Two exemplary im-
ages of a bone cyst on coronal Short Time Inver-
sion Recovery (STIR) and Fast Spin-Echo (FSE) T1-
weighted series are shown in Figure 1. In the radio-
logical diagnosis the comparative analysis of both the
series is utilised. Due to this fact, first, different 3-
D multifeature clustering procedures (McLachlan and
Peel, 2000; Heo and Gader, 2010) have been applied.
However, none of the implemented multifeature algo-
rithms has yielded satisfactory final segmentation re-
sults. Therefore, a fuzzy inference system simulating
experts reasoning, described in the following sections,
has been developed.
Figure 1: A bone cyst visualised on a single slice coming
from two different MR coronal series: left STIR, right
FSE T1-weighted.
Let us assume that there are two reference regions
selected on a single slice: tumour area and the back-
ground, respectively. The areas are then transferred
into both the analyzed modalities. Let the already
given regions constitute the expert knowledge. Due to
the fact that the grey intensity levels constructing the
tumours areas vary depending on the analyzed lesion
and its location in the patients body, the fuzzy rules
and dictionary are adaptively created for each single
tumour case. The varying grey intensity levels build-
ing tumour as well as background areas on both MR
sequences are described using the Gaussian Mixture
Model. The obtained models are then used both in a
fuzzy system dictionary and the rules base. The crisp
value at the output of the developed fuzzy inference
system is the fuzzy affinity value µ
K
(o,e).
3 GAUSSIAN MIXTURE MODEL
Gaussian Mixture Model (GMM) is a semi-
parametric technique, which enables estimating a
probability density function with a mixture distribu-
tion (McLachlan and Peel, 2000; Dempster et al.,
1977), defined as a weighted sum of its components.
Let be a set of N vectors x
n
= [x
1
n
,x
2
n
,...,x
D
n
]
T
,
n {1, . . . , N}, where D is the dimensionality of fea-
ture space. Consider a mixture model with K(K > 1)
components in R
n
for n 1. The probability density
function of vector x in the mixture is given as
p(x) =
K
k=1
π
k
p
k
(x), (9)
where p
k
(x) is the density of k-th component and
π
k
[0, 1] are the mixing proportions coefficients ful-
filling
K
k=1
π
k
= 1. (10)
In the Gaussian Mixture Model each group of the
data is assumed to be generated by a normal probabil-
ity distribution
p
k
(x) =
1
(2π)
D
2
det(Σ
k
)
1
2
exp
1
2
(x λ
k
)
T
Σ
1
k
(x λ
k
)
,
(11)
where λ
k
and Σ
k
are the parameters of D-dimensional
normal probability distribution N(λ
k
,Σ
k
), mean val-
ues vector and covariance matrix, respectively.
The maximum likelihood estimator of parameter
Θ = {Θ
1
,Θ
2
,...,Θ
K
}, where Θ
k
= {λ
k
,Σ
k
}, of a
parametric probability distribution is found using the
Expectation-Maximization (EM) algorithm (Demp-
ster et al., 1977). Since the EM procedure is dedicated
to incomplete data sets analysis, it iteratively alter-
nates between finding the greatest lower bound to the
likelihood function, making guesses about the com-
plete data and then maximizing this bound by finding
the Θ that maximizes p(x|Θ) over Θ.
FuzzyModel-basedAlgorithmfor3-DBoneTumourAnalysis
187
The EM algorithm requires starting points as well
as clusters number selection. The required parame-
ters are estimated applying the unsupervised cascade
clustering procedure and Kernelised CS cluster valid-
ity measure discussed in detail in (Czajkowska et al.,
2012).
In the proposed segmentation procedure the adap-
tively generated bone tumour as well as background
model constitute the basis for fuzzy inference system.
The obtained components parameters are used in the
fuzzy dictionary, which defines the membership func-
tions of fuzzy rules. The combination of different
components building particular image regions is the
basis for fuzzy rules generation.
4 FUZZY INFERENCE SYSTEM
There exist different fuzzy reasoning systems de-
scribed in literature (Yamaguchi et al., 2010; Hata
et al., 2000; Siler and Buckley, 2005) and also applied
to medical tasks. The basic structure of such systems
consists of three components: dictionary defining the
membership functions, base of fuzzy IF-THEN rules
and reasoning mechanism.
Historically the first fuzzy control system, based
on Zadeh’s formulations from 1973, was introduced
by Mamdani in 1976. The input numbers are there
translated into linguistic terms and the fuzzy rules
map them onto linguistic terms describing the system
output. Then, the output linguistic terms are trans-
lated back into the numbers. The procedures of trans-
lations are known as fuzzification and defuzzification,
respectively. A typical fuzzy rule in such a system is
constructed as follows:
IF input1 is A
1
i
AND input2 is A
2
i
T HEN out put is B
i
(12)
It tries to formulate the expert knowledge using some
linguistic rules. An exemplary rule dedicated to the
task of bone tumour segmentation can be simply de-
scribed as:
IF the intensity level o f the area
in T 2 weighted series is very high
AND the intensity level o f the area
in T 1 weighted series is very low
THEN the analyzed region
might be a tumour
(13)
There are different combinations of grey intensity lev-
els suggestive of bone tumour defined by the experts
and consequently different linguistic rules connected
with them. Simultaneously, there exists a set of lin-
guistic rules defining the healthy tissues. The devel-
oped fuzzy inference system attempts to describe the
majority of them.
Let the fuzzy sets in the fuzzy premises of i-th rule
be given as A
1
i
and A
2
i
, respectively and the fuzzy set
in the conclusion of i-th rule is denoted as B
i
. In the
exemplary radiologist reasoning rule, the fuzzy sets
A
1
i
and A
2
i
are given as ”high” and ”low” and B
i
as
”might be tumour”.
The fuzzy control algorithm developed by Mam-
dani is based on two concepts: fuzzy implication and
compositional rule of inference (Kickert and Mam-
dani, 1978). Assume two fuzzy sets: A of the uni-
verse of discourse X and B of Y defined by their fuzzy
membership functions µ
A
and µ
B
. The membership
function of a fuzzy implication S: ”IF A then B is
then defined as
µ
s
(x,y) = min[µ
A
(x);µ
B
(y)], x X, y Y. (14)
For such given implication S, fuzzy set B
of the uni-
verse of discourse Y inferred by a given fuzzy set A
of X, has a membership function estimated as
µ
B
(y) = max
x
min[µ
A
(x);µ
s
(x, y)], x X, y Y.
(15)
In fuzzy systems found in research applications
there are different rules describing one phenomenon.
When the rules conditions are matched, a set of ac-
tions will be activated. Each rule, with the antecedent
non-zero matching degree, contributes an output with
the activation value equal to it. The final system out-
put taking into consideration all the activated rules is
constructed using an aggregation operation. Its most
common implementation is operator max, however
there exist different aggregation operators found in
real applications, like algebraic sum or the bounded
product.
Coming back to the bone tumours analysis, the
already described fuzzy system is used in the fuzzy
connectedness analysis in order to estimate the fuzzy
affinity value of the spels connection, instead of the
functions given by (4) and (5).
5 ALGORITHM
Before the segmentation procedure begins, thanks to
the positioning information provided by the DICOM
header, the positions of voxels belonging to the two
analysed MR series are matched.
The segmentation procedure starts on
the basis of exemplary region selection
performed by an expert. The automated
part of analysis begins with the adaptive
3-D filtering method (Perona et al., 1994). The
there required parameters are adaptively estimated
based on the assumptions given in (Positano et al.,
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188
2000). The goal of this analysis step is firstly the
reduction of noise and thereby an increase in the
signal-to-noise or contrast-to-noise ratios while
maintaining the edge lines. Secondly, as a result of
smoothing the objects areas the number of groups
in the clustering procedure, being the next step,
decreases and the analysis is not sensitive to outliers.
The main part of performed analysis constitutes of
four steps discussed in previous sections, whose com-
bination is shown on the block diagram in Figure 2.
Figure 2: The flow chart of 3-D bone tumours segmentation
procedure
First, based on the reference expert selections,
personalized GMMs of bone tumour and background
areas are generated. The detailed discussion of the al-
gorithm is given in section 3. Let the obtained GMMs
of tumour area be given as G
1,2
t
and of the background
as G
1,2
b
, respectively. Both GMM pairs are the sets of
mixture components parameters θ and voxels C clas-
sified into each of K
t
or K
b
groups
G
i
t
= (θ
i
1
t
,C
i
1
t
),(θ
i
2
t
,C
i
2
t
),...,(θ
i
K
t
,C
i
K
t
),
G
i
b
= (θ
i
1
b
,C
i
1
b
),(θ
i
2
b
,C
i
2
b
),...,(θ
i
K
b
,C
i
K
b
),
(16)
where index i = {1,2} refers to two simultaneously
analysed MR sequences.
Based on them, the input membership functions
describing the intensity levels constituting tumour as
well as background areas are defined. An exemplary
set of membership functions obtained for a bone cyst
in STIR and T1-weighted sequences (Figure 1) is vi-
sualised in Figure 3. The membership functions de-
fined for the tumour area are marked with the black
solid lines and the membership functions defined for
the background are given by the grey dashed lines.
Figure 3: An exemplary set of membership functions gener-
ated for a bone cyst in STIR (top) and T1-weighted (down)
sequences. The membership functions defined for the tu-
mour area are marked with the black solid lines and the
membership functions defined for the background are given
by the grey dashed lines.
Since the fuzzy connectedness analysis is used in
the segmentation step, the system inputs should cause
two adjacent spels to obtain their affinity value. The
functions given by (4) and (5) take into consideration
the mean intensity value 0.5(I(e)+I(d)) and gradient
|I(e)I(d)|. Since the attempts of modelling gradient
values characterising tumour or healthy tissues have
not provided any useful information, the inputs to the
fuzzy system are defined as x
i
= 0.5(I
i
(e) + I
i
(d)).
Two membership functions in the conclusions of
rules are shown in Figure 4. The output of the system
is the affinity value of two adjacent spels. The mem-
bership function visualised using the black solid line
defines the ”high” affinity and the dashed line defines
the ”low” affinity of spels connection. Moreover, to
reduce the computation time associated with the rela-
tive FC analysis, the meaning of ”big” affinity value is
”it might be tumour”. Based on the graph of the func-
tions in Figure 4, the threshold defining the tumour
area can be set to 0.45.
Figure 4: An exemplary set of membership functions on the
output of the fuzzy inference system. The black solid line
defines the tumour and the grey dashed line represents the
background.
Let the fuzzy sets in premises referring to G
1,2
t
and G
1,2
b
are given as A
i
k
t
and A
i
l
b
, and the fuzzy sets in
conclusions as B
h
”high” and B
l
”low”. Then, on
the basis of sets G
1,2
t
and G
1,2
b
and all the positions of
voxel c the unique fuzzy rules R
l
t
, l {1, 2,...L} and
R
p
b
, p {1, 2, . . . P} defining tumour and non-tumour
FuzzyModel-basedAlgorithmfor3-DBoneTumourAnalysis
189
areas, respectively, are generated as follows:
1: if c T and c C
1
k
t
and c C
2
k
t
, where T is the set
of reference tumour voxels then
2:
R
l
t
: IF x 1 is A
1
k
t
AND x2 is A
2
l
t
T HEN µ
K
(e,d) is B
h
(17)
3: end if
4: if c T and c C
1
k
t
and c C
2
k
t
, where T is the set
of reference background voxels then
5:
R
p
b
: IF x1 is A
1
k
b
AND x2 is A
2
l
b
T HEN µ
K
(e,d) is B
l
(18)
6: end if
For each pair of the adjacent voxels the output linguis-
tic value is then translated into their fuzzy affinity. In
the defuzzification step the center of gravity method is
employed. Using the precomputed affinity tables, the
multiseeded FC algorithm described in (Badura et al.,
2011) is performed.
To reduce the false positive regions in the case
when the tumour is connected with the healthy tissues
having similar characteristics, a convex hull-based
postprocessing technique is applied. Starting from the
reference slice the there obtained tumour convex hull
is then mapped into the adjacent slices. The compar-
ison of areas of tumour like regions covered and un-
covered by the convex hull provides the information
concerning the final segmentation results.
6 EXPERIMENTS AND RESULTS
To evaluate the ability of developed methodology, the
database consisting of 27 examinations of 18 patients
studies has been used. The therein contained cases
have included 5 types of bone tumours: chondromas,
Ewing’s sarcomas, osteosarcomas, bone cysts and
chondrosarcomas. In total, 413 pairs of slices have
been analysed. An individual pair have consisted of
T1-weighted, T1-weighted contrast enhanced and fat
saturated, T2-weighted or STIR sequences in differ-
ent MR projections: axial, sagittal and coronal. The
FC threshold values have been set to 0.45 and 0.5.
All the obtained results have been discussed with
an expert, who jugged them on each slice in each ex-
amination. As a result the obtained image regions
have been divided into three classes: true positive
(TP) the coherent areas containing a correctly indi-
cated tumour, false positive (FP) a coherent region
containing healthy tissues incorrectly classified as tu-
morous, false negative (FN) a coherent region con-
taining tumour areas incorrectly classified as healthy
tissue.
The accuracy of presented segmentation proce-
dure has been estimated based on the following simi-
larity coefficient
DV =
FP + FN
T P + FN
, (19)
yielding the value equal 0 when the segmentation re-
sults are fully correct. The obtained DV value for the
bone tumours database has been equal to 0.12, which
is sufficient for computer assisted diagnosis systems.
Exemplary results for 3 different types of bone tu-
mours are shown in Figures 5 - 7.
The original fuzzy connectedness algorithm (FC1)
described in (Udupa et al., 2002) as well as its modifi-
cation (FC2) developed in (Badura et al., 2011) were
used to compare the obtained results, which were cat-
egorized into two groups: the segmentation results
in the homogeneous and in-homogeneous image se-
ries. The numerical results (DV values) are summa-
rized in the Table 1, where the last column (FIS) pro-
vides the results obtained using the proposed method-
ology. The first row of Table 1 shows that the segmen-
tation results obtained for homogeneous image data
are comparable with other methods. The second row
proves a superiority of the proposed method over an-
other approach described in literature, which results
are insufficient for computer assisted diagnosis sys-
tems and not acceptable by a radiologist.
Table 1: Accuracy of different segmentation procedures
DV coefficient.
FC1 FC2 FIS
Homogeneous
Series (22) DV 0.16% 0.13% 0.13%
In-homogeneous
Series (5) DV 0.6% 0.5% 0.11%
Figure 5: Final segmentation results of knee Enchondroma
visualised on a single slices of axial MR series: left T2
Blade FS, right T1 TSE.
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190
Figure 6: Final segmentation results of spines Ewing’s sar-
coma visualized on a single slices of sagittal MR series: left
T1+C SE FS, right STIR.
Figure 7: Final segmentation results of tibias Osteosarcoma
visualized on a single slices of coronal MR series: left T2
FRFSE FS, right T1 FSE.
7 CONCLUSIONS
This paper introduces a 3-D multifeature bone tu-
mours segmentation method in MR images. The in-
sensitive to bone tumour location and type algorithm
combines Gaussian Mixture Model and fuzzy infer-
ence system in the fuzzy connectedness analysis. The
proposed procedure has been tested on the database
of real bone tumour cases consisting of 27 exami-
nations of 18 patients, a single examination contain-
ing two different MR series. The obtained segmenta-
tion results encourage to further develop this method.
The presented system provides a basis for develop-
ing an adaptively learning algorithm, training being
based on the currently analysed and verified cases.
The problem still remaining to be solved is the nor-
malisation of MR sequences so that they can be com-
pared. The plans for further work take into consider-
ation expanding the database with new tumour cases
and involving in the analysis new features like tex-
ture. The detailed radiological consultation will en-
able developing fuzzy IF-THEN rules base and rea-
soning mechanism. In order to improve the segmen-
tation results some fuzzy rules interpolation technique
is also planned to be introduced.
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