Melanoma Detection System based on a Game Theory Model
Djamila Dahmani, Slimane Larabi, Sihame Djelouah, Nafissa Benhebbadj and Mehdi Cheref
Computer Science Department, USTHB University, BP 32 EL ALIA, Algiers, Algeria
Keywords: Melanoma, Skin, ABCD, Zero-sum Game Theory.
Abstract: We propose in this paper a new method for Melanoma detection (the most dangerous form of skin cancer)
based on ABCD medical procedure. The ABCD features play a crucial role in the accuracy of diagnosis
rates. However, the search for such distinctive data remains difficult, because of the small variability in the
appearance of benign and cancerous skin lesions. To cope with this problem, each feature is calculated
using different formulas. Then if all the used formulas agree about the lesion classification, it will be
classified according to the full agreement. Otherwise, for doubtful pigmented skin lesions, the game theory
model is applied for final decision. The game model proposed in our work, estimates that the conflict is
between two agents (melanoma and non-melanoma). The different formulas applied in the computation of
the features A, B, C, and D are the pure strategies. The value sign in the mixed extension of the game
allows classifying correctly the skin lesion. The method was tested on two publically available databases
PH2 and ISIC, the obtained results are promising.
1 INTRODUCTION
Melanoma is one of the most aggressive human
tumors. Moreover, Melanoma has a cure rate of
more than 95% if detected in early stage (Roma et
al., 2007). Skin cancer recognition on computer
Aided Diagnostic (CAD) has been an important
research area. The objective of CAD systems is to
provide a computer output as second opinion in
order to assist the radiologists on interpretation to
improve the accuracy and reduce the image reading
time (Doi, 2005). New approaches are developed to
help earlier diagnostics. Dermoscopy is one of the
most used tools in the precocious detection of
Melanoma. Dermoscopy (also known as
dermatoscopy or epiluminescence microscopy) is a
method of acquiring a magnified and illuminated
image of a region of skin for increased clarity of the
spots on the skin (Binder et al., 1995). The use of
dermoscopy gives a magnification of the images of
the nevus lesions and it permits the analysis of
particular characteristics of the lesion, including
symmetry, size, borders, presence and distribution of
color features. The typical computer-aided diagnosis
(CAD) pipeline for auto-mated skin lesion diagnosis
(ASLD) from digital dermoscopic images can be
divided into the following steps (Wighton et al.,
2011): Image acquisition, Noise and artefact
filtering, Lesion segmentation; Feature extraction,
and Classification.
The medical diagnostic of skin lesions based on
dermoscopy used ABCD rule (Stolz et al., 1994), 7
point-checklist (Argenziano et al., 1998) and
Menzies’ method (Menzies et al., 1998). These cues
are sometimes called the letters of the dermoscopic
alphabet since there are features used for the final
diagnostic decision. The ABCD rule is proved that it
can be easily learned and rapidly calculated and has
been proven to be a reliable method providing a
more objective and reproducible diagnosis of
melanoma (Stolz et al., 1994).
In this paper each feature (Asymmetry,
irregularity of Border, presence of specific Colors,
and lesion shape and size) is calculated using
different formulas, thus reflecting diverse aspects of
the feature and not giving necessarily the same
result. At first step, if the methods used all the
characteristics are unified on the same classification
of the lesion, it will be classified according to this
agreement; otherwise a game theory model is
employed to take decision about the lesion type. The
idea behind the proposed model is to consider the
disagreement of the formulas in the lesion
classification as a zero-sum game where the
melanoma and non-melanoma are considered
players and the different formulas applied in the
computation of the characteristics A, B, C and D
Dahmani, D., Larabi, S., Djelouah, S., Benhebbadj, N. and Cheref, M.
Melanoma Detection System based on a Game Theory Model.
DOI: 10.5220/0008879807030711
In Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2020) - Volume 5: VISAPP, pages
703-711
ISBN: 978-989-758-402-2; ISSN: 2184-4321
Copyright
c
2022 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
703
provide strategies. Then an efficient utility function
is proposed for modeling the discord and attributes
the lesion to the most persuasive player namely the
melanoma or non-melanoma class.
One important difference of our approach
compared to previous works is that the ABCD
features are taken separately, and each feature is
computed with various manners to cope with the
problems of the imprecise segmentation of skin
lesions, and the narrow variability in the appearance
of benign and cancerous skin lesions. The zero-sum
game theory architecture with an appropriate utility
function is then used to model this variability and to
take decision about the lesion classification.
The paper is organized as follows, the section 2 is
devoted to the related works, the section 3 to the
explanation of the proposed method and finally the
experiment results and discussion will be presented
in section4.
2 RELATED WORKS
Recently there is a big interesting in development of
computer-aided skin diagnostic systems (Moradi et
al., 2019; Sadri et al., 2017; Gu et al., 2017; Bi et al.,
2016; Kruk et al., 2015; Pennisi et al., 2016). These
approaches can be classified into two categories: (i)
Dermoscopic based approaches and, (ii) Pattern
recognition based approaches. (Pennisi et al., 2016)
proposed an automatic skin lesion segmentation
algorithm based on Delaunay triangulation. The
segmentation approach produced better results in
case of benign lesions. The authors in (Gu et al.,
2017) proposed a melanoma detection system based
on Mahalanobis distance learning and constrained
graph regularized non-negative matrix factorization.
The method achieved 94,43% in sensitivity and
81,01% in specificity. The authors in (Sadri et al.,
2017) proposed a technique based on fixed wavelet
grid network (FWGN). The construction of FWGN
is performed using D-optimality orthogonal
matching pursuit (DOOMP). (Bi et al., 2016) used
an automatic melanoma detection technique for
dermoscopic images via multi-scale lesion-biased
representation (MLR) and joint reverse classification
(JRC). Skin lesions are represented using closely
related histograms. JRC model provides distinctive
additional information for melanoma detection. The
method proposed in (Kruk et al., 2015) used
extended set of diagnostic features describing the
image of skin lesions combined with different
solutions of the classifiers. The authors resigned
from the ABCD features trying to find more
powerful descriptors. The results of the proposed
system are: accuracy of 89.5%, sensitivity of 95%
and specificity of 88.125%. Moradi and Mahdavi-
Amiri (Moradi et al., 2019) proposed a system of
skin lesion segmentation and classification based on
novel formulation for discriminative kernel sparse
coding jointly learns a kernel-based dictionary and a
linear classifier. The method is insensitive to noise
and image conditions and can be used effectively for
challenging skin lesions.
3 METHODS
The proposed method consists from some steps. At
first the dermoscopic image is pre-processed to be
segmented. The salient features are then extracted
from segmented image. Finally the classification
phase is performed using a zero-sum game theory
modelling.
3.1 The Pre-processing Step
In this step, a method of removing hair and artefacts
was applied to facilitate future treatments and to not
alter the results. At first, a median filter was applied
to the image, and then a morphological
transformation was used to close the hair pixels with
the pixels of its surrounding area and keep the shape
of the lesion. The closing operation was performed
separately on the three RGB color channels of the
image (see Figure 1).
3.2 Segmentation Step
After pre-treatment, three algorithms were applied
namely: the color thresholding segmentation to
identify the pixels belonging to the skin around the
lesion, along with SLIC (Simple Linear Iterative
Clustering) Superpixels algorithm (Achanta et al.,
2012) and Otsu segmentation algorithm (Otsu, 1979)
to segment the lesion region.
3.2.1 Color Thresholding Segmentation
Several methods of segmentation of the skin into
color images are available in the literature. The
simplest methods define limits in the color space
chosen to identify skin clusters. The main advantage
of these methods is that they do not require a
training phase. However, it is difficult to define the
limits that work well by considering a single color
space. For this reason, in our algorithm, we
converted the image to HSV and then we set 140
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distinct thresholds that include multitude of skin
colors.
Figure 1: (a) Original image, (b) The image after the
processing step.
3.2.2 SLIC Segmentation Algorithm
Each region is represented by a Superpixel created
by the SLIC algorithm (Achanta et al., 2012). The
advantage of this algorithm is that it generates
compact and homogeneous regions of uniform size,
regular shape, and almost respecting the limits of the
lesion. However, the choice of the appropriate
segmentation scale is not obvious because the lesion
as well as some details in the image may appear at
different sizes. For this reason we applied a third
method of segmentation, on the image result
obtained by SLIC algorithm.
3.2.3 Otsu Segmentation Algorithm
The Otsu method (Otsu, 1979) is a quick and simple
threshold method that automatically calculates a
threshold value from the image histogram. The
threshold value is then used to classify the pixels in
the image based on their intensity.We used Otsu
segmentation on the SLIC result, and then applied a
morphological closure to remove the outliers. The
figure 2 presents an example from PH2 database
(Mendonc et al., 2013) of the segmentation step.
3.3 Features Extraction
The ABCD is clinical guideline used by the
dermatologists for the skin lesions diagnostic. The
measures A, B, and C reflect the geometric
proprieties of skin region and C is linked to the
chromatic and lightness characteristics. The ABCD
requires subjective evaluation of the different
aspects of a skin lesion (Ma et al., 2017). In order to
cope with the subjective evaluation, and
classification decision we integrate in this paper
zero-sum game theory modeling. At beginning, each
composite feature (A, B, C, and D) is computed with
different mathematical formulas and so translate
various aspects of each characteristic. In the flowing
the computation details will be given.
Figure 2: (a) Initial image, (b) color thresholding
segmentation, (c) SLIC segmentation algorithm, (d) Otsu
segmentation algorithm.
3.3.1 Asymmetry
According to dermatologists, melanomas develop
anarchically (they are asymmetrical), while benign
tumors are symmetrical.
In order to obtain good result we used the
following methods to calculate the asymmetry of the
lesion:
Best Fit Ellipse: based on the method proposed
in (She et al., 2007), one way to measure asymmetry
is to fold the contour of the lesion around the chord
of the best-fitting ellipse and looking for the
difference (the non-overlapping region). That is
calculated as following:
𝐴
=
∆𝑆
𝑆
× 100
(1)
Where ∆S is the difference area surface and S is
the lesion surface.
Principal Axis: this asymmetry index is
calculated using the algorithm presented in
(Andreassi et al., 1999). It is based on the
computation of the smallest difference between the
image area of the lesion and the image of lesion
reflected from the principal axis.
𝐴
=
𝑆
𝑆
× 100
(2)
Where S’ is the difference area.
Main Axes: at first the shape is translated so
that the lesion will be placed in the center of the
image. Then the image is rotated to align with the
main axes. The lesion will be divided into four sub
regions. The asymmetry value is obtained by
subtracting the reflected area on one side of the axis
of the reflected form, giving two area differences. It
is given by the formula:
𝐴
=
∆S

S
× 100
(3)
Melanoma Detection System based on a Game Theory Model
705
where ∆𝐒
𝐦𝐢𝐧
is the smallest difference of areas.
Centered Sub Regions: this is the same
method as the previous one, except that this time the
lesion was translated so that the center of the image
coincides with the center of mass of the lesion as
proposed in (Stoecker et al., 1992).
3.3.2 Border
Benign lesions are generally defined by clear limits,
while melanomas are defined by very contrasting
irregular boundaries. We use four features to
characterize the border irregularities.
Compact Index: the compact index (CI) of a
skin lesion is an important aspect to consider, when
looking for melanoma. The factor (CI) indicates how
much the skin lesion looks like a circle. It is defined
as:
CI=
P
S
(4)
P is the lesion perimeter and S the total area.
Fractal Dimension: the fractal dimension
measures how the details change with scale, it
indicates the complexity of fractal patterns. It is
obtained by the box counting algorithm. The lesion
boundary is determined then covered with a grid,
and finally the number of occupied boxes in the grid
is counted. It is defined by the formula:
d

=
log
(
b
)
log
(
r
)
(5)
Where b is the number of smallest boxes that
covered the edge line and r is the inverse of the
smallest box side length.
Length Contour: If the outline is wide enough
then: either the lesion is large, or it is small and its
borders are irregular, or it is large with irregular
edges, and in all three cases it is a sign of
abnormality.
Regularity Index: The regularity index
allows the calculation of the uniformity of the
form. It is computed by the equation (6).
r=
P
S
(6)
Where P is the lesion perimeter and S the total area.
3.3.3 Color
Colors Number: the pigmentation of a lesion
can be characterized by several colors. Five to six
colors may be present in a malignant lesion.
Potential colors of melanoma are: White, Red,
Black, Light Brown, Dark Brown and Grey Blue.
For each color space we have defined 6 intervals to
threshold its 3 components. The idea is to convert
the image to HSV (YCbCr, or HLS) and then scan
all the pixels of the lesion by calculating the
percentage of belonging of each of the 6 colors, if
that percentage is above a certain threshold then it is
said that this color exists.
Kurtosis: the kurtosis value measures whether
the distribution of pixels is maximum or flat
compared to a normal color distribution. It is the
fourth standardized moment, it is calculated by the
formula:
𝜎
=
1
𝑁
(
𝑝
−𝑥
̅
)


(7)
𝑝
is the i
th
pixel intensity, 𝑥̅ is the mean intensity
and N is the total amount of pixels within the skin
lesion.
3.3.4 Diameter
Melanomas usually start with a diameter of more
than 6-7 millimetres. For the calculation of diameter
we used 4 different methods.
Minimal Enclosing Circle: the radius of the
minimal circle enclosing the lesion will be
considered as the diameter of this lesion.
Lengthening Index: this measure is used to
describe the lengthening and degree of anisotropy of
the lesion. The ratio between moment of inertia δ'
around the principal axis, and the moment of inertia
δ'' around the secondary axis quantifies the rate of
elongation L given by the formula:
L=
δ
δ

(8)
δ
=
m

+m

((
m

− m

)
+4
(
m

)
)
2
(9
)
δ

=
m

+m

+
((
m

−m

)
+4
(
m

)
)
2
(10)
Where m_pqdenote the (p + q)th order geometric
and central moments of the lesion.
Contour Diameter: The main idea is to find
the circle whose perimeter is equal to the perimeter
of the lesion, so the diameter of the lesion will be
equal to the length of the radius of that circle.
Distance between Extreme Points: To
calculate the diameter in this method we first looked
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706
for the 4 end points (top, bottom, left and right), then
we calculated the distance between the high and low
points and the distance between the left and right
points and kept the maximum of the two which is
considered as the diameter.
3.4 Classification and Zero-sum Game
Theory Modeling
The features explained in the section 3.3 are used
with appropriate thresholds to classify a given
lesion. The main idea is that if all the characteristics
agree about the nature of the lesion, it will be
classified according to this agreement. Otherwise,
we propose a game theory modeling to classify
correctly the doubtful pigments. A lesion will be
considered doubtful if at least one formula related to
a given characteristic A, B, C, or D classifies it
differently from others. The game proposed will be
established between two gamers melanoma and non-
melanoma players, where the doubtful pigment is
considered a disputed territory. Each player would
like to conquer all the identical territories to its
nature and will face its own defeat if he penetrates
the opposite territory. This game would perfectly fit
into a zero-sum game (one player's loss is equal to
the other player's gain). The pure strategies of each
player are defined from the different formulas used
in the computation of the features A, B, C and D.
For each class of formulas related to a given
feature: Asymmetry, Border, Color or Diameter, the
concatenation of the formulas which classified the
doubtful lesion as melanoma is considered as
strategy of melanoma player related to this feature.
The concatenation of the rest of formulas in this
class is considered strategy of the non-Melanoma
player. So we obtain strategies from type
“Asymmetry-Melanoma”, “Asymmetry-non-
Melanoma”, “Border-Melanoma”, “Border -non-
Melanoma”, “Color-Melanoma”, “Color-non-
Melanoma”, “Diameter-Melanoma”, “Diameter-
non-Melanoma”.
In particular case, where all the computation
formulas of a given feature A, B, C or D classify the
doubtful lesion Melanoma (non-Melanoma
respectively) the strategy of this feature will be
omitted from the set of strategies of the non-
melanoma player(Melanoma player respectively).
The saddle point in the mixed extension of this game
will represent a compromise agreement of the two
players (Melanoma and non-Melanoma), where the
territory will be granted to the most persuasive
player, according to the mixed value of the game.
The mathematical formulation of the problem
can be presented as follows:
We define the proposed zero-sum game by the
given elements=
(
J,S
,u
)
where:
J=
Melanoma palyer, non − Melanoma player
:
the set of players.
S
for i=1,2 are the sets of pure of strategies for
each player in a doubtful lesion D.
u is the utility function explained in the following.
3.4.1 Utility Function
The payoff function is the main subject of this
research effort, how could we define an appropriate
payoff function providing a meaningful result?
The computation of the utility function is based
on the similarity between the characteristics of the
lesion and those of melanoma sample images. This
similarity was quantified using a correlation
distance. In order to define the correlation distance,
we determine for each strategy
𝑠
the melanoma
data matrix
𝑀
. The lines of 𝑀
are consisting of
the characteristic vector, associate to the strategy
𝑠
,
computed from sample of images classified as
melanoma by all formulas presented in the section
(3.3).
We notate 𝑋
and 𝜎
the average and the standard
deviation of the 𝑗

variable in the melanoma data
matrix data 𝑀
given by the equations:
𝑋
=
𝑋


;
𝜎
=
(𝑋


−𝑋
)
/
….
(11)
Where 𝑚 is the number of melanoma lesions in
the set of sample melanoma images, and 𝑛 the
dimension of the features vector used in the
strategy 𝑠
.
The center of gravity of the matrix 𝑀
is given
by the equation:
𝐺
=
(
𝑋
,𝑋
,…,𝑋
)
(12)
The standard deviation of the
matrix 𝑀
is given by
𝜎
=
(
𝜎
,…,𝜎
)
(13)
-Then the centered and standardized matrix obtained
from the matrix 𝑀
is computed by the formula:
𝑍
=
𝑋

𝑋
𝜎
𝑋

𝑋
𝜎
⋮⋱
𝑋

𝑋
𝜎
𝑋

𝑋
𝜎
(14)
Melanoma Detection System based on a Game Theory Model
707
-The correlation matrix is computed from the
formula:
𝑅
=
1
𝑚
𝑍
𝑍
(15)
We note 𝑇
the features vector of 𝑫 in the 𝑠
description:
𝑇
=
𝑇
𝑇
(16)
The 𝑇
the centered and standardized vector
according to the data the matrix 𝑀
, is given by
𝑇
=
𝑇

𝜎
𝑇

𝜎
(17)
-Let be the vector 𝑌
a vector belonging to the
matrix 𝑍
such that:
𝑌
∈𝑎𝑟𝑔min
∈
𝑇
−𝑌
, where
‖‖
is
the Euclidian distance.
-Finally, we define the vector 𝑉
such that 𝑉
=
𝑇
−𝑌
.
The correlation distance 𝑑
which characterizes
the similarity between the features vector of the
doubtful lesion 𝑫 and the data matrix 𝑀
of
melanoma individuals is then determined by the
relation:
𝑑
,
=𝑉
𝑅
𝑉
(18)
The value of 𝒅
𝒔
𝒊,𝑫
will be close to zero as long as
the 𝑇
is similar or close to the characteristic vectors
of the data matrix 𝑀
, this means that D is similar or
approaching the melanoma lesion characteristics.
Otherwise the value of 𝒅
𝒔
𝒊,𝑫
will be strongly greater
than zero, this means that D is not similar and very
different from the characteristic vectors of the data
matrix 𝑀
, and this involves that the entity 1/𝑑
,
roll a way the melanoma’s characteristics when it
approaches the zero.
Since the melanoma similarity aspect had been
modeled, the utility function in a doubtful lesion 𝐷
can be formulated by the formula.
𝑢
(
𝑠
,𝑠
)
=
1
𝑑
,
−𝑑
,
(19)
So, the sign of the real 𝑢
(
𝑠
,𝑠
)
is positive if the
doubtful lesion is closer to the melanoma and
negative otherwise. This fact translates the zero-sum
game interaction between the melanoma and non-
melanoma players.
3.4.2 Saddle Point or Nash Equilibrium in
the Zero-sum Game
After the elaboration of the game matrix 𝐴 in a
doubtful lesion, the computing of the saddle point or
the Nash Equilibrium, will allow us to settle the
doubt and take decision about the lesion’s nature.
The value in a zero-sum game is the payoff value of
the optimal strategies for each player. Therefore, the
fairest manner to assign the doubtful lesion to
melanoma or non-melanoma class is to focus only
on the sign value of the game. If this value is equal
to zero the game is fair, if it is positive, the game
favors the melanoma player, while if it is negative;
we say the game favors the no-melanoma player.
The value doesn’t always exist in pure games, so
we use the mixed (randomized) extension of the
game that we note
.
can be described by the
given elements
=(𝐽,
(
𝑆
)
,𝜇) where
(
𝑆
)
is the
set of all probability distributions over 𝑆
.
(
𝑆
)
=𝑥
|
|
:𝑥
≥0 𝑒𝑡 𝑥
=1
|
|
(20)
𝑓𝑜𝑟 𝑖=1,2
𝜇=𝐸(𝑢
(
𝑥,𝑦
)
) is obtained from the payoff
function 𝑢 of the equation (18) in the zero-sum pure
game and the mathematical expectation of the
profile
(
𝑥,𝑦
)
such us
(
𝑥,𝑦
)
∈∆
(
𝑆
)
×∆
(
𝑆
)
According to the notations above:
𝜇=𝐸𝑢
(
𝑥,𝑦
)
=𝑥
𝐴
𝑦 (21)
where A is the payoff matrix of the game
determined in previous subsection 3.4.1.
In his fundamental Minimax Theorem (the Main
Theorem of the theory of Games) (Neumann, 1928)
established the existence of a unique value v in
mixed finite games such that:
max
∈∆
(
)
min
∈∆
(
)
𝑥
𝐴
𝑦=min
∈∆
(
)
max
∈∆
(
)
𝑥
𝐴
𝑦=𝑣
(22)
and some optimal mixed strategies 𝑥
,𝑦
(Nash
equilibrium profile (𝑥
,𝑦
) ) such that the expected
payoff 𝑣
is calculated by equation (22).
(
𝑥
)
𝐴
𝑦
=𝑣
(23)
Thus 𝑣
is the maximumfloor of the Player 1
and minimum “ceiling” of player 2.
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708
A solution (𝑥
,𝑦
,𝑣
) of the matrix game 𝐴 can be
obtained by the resolution of linear optimization
problem. It was proven that there is a polynomial time
algorithm for finding a mixed Nash equilibrium in a
two-player zero-sum game, for more details see
(Nisan et al., 2007). In this paper, we use the sign of
value 𝑣
(the expected payoff) in a doubtful lesion to
classify the patch in melanoma (first player) or non-
melanoma (second player) class. If the value 𝑣
=0
the lesion is attributed to melanoma class for security
measure.
4 EXPERIMENTAL RESULTS
The evaluation of the model performance is very
important and the most commonly used performance
measure is the classification score. However, for
datasets with large class imbalances, a classification
score does not make much sense. Instead (Receiver
Operating Characteristic) ROC curves offer a better
alternative.
For the evaluation of our system and the
implemented methods, we followed the approach
developed by the researchers, namely the calculation
of the accuracy, the recall, the specificity, and the
estimation of the ROC curves.
4.1 Used Datasets
In order to test the proposed method, we used the PH
2
dataset (Mendonc et al., 2013) released by the
University of Porto, in collaboration with the Hospital
Pedro Hispano in Matosinhos, Portugal. This dataset
contains 200 RGB dermoscopic images of
melanocytic lesions, including 80 common nevi, 80
atypical nevi, and 40 melanomas. The method is also
tested on the ISIC 2017 dataset (Codella et al., 2017)
which contains 2000 dermoscopic images.
4.2 Comparison of the Game Theory
Modeling with the Features ABCD
In this section, we first compare the proposed zero-
sum game theory model to the features ABCD. We
note that for each characteristic A, B, C, and D we
take the best result obtained using the formulas
presented in the section (3.4). The comparison was
performed using the ROC (Receiver Operating
Characteristic) curve; the quality of classification is
assessed using the metric AUC (Area Under the
receiver operating characteristics). The results for
PH2 (Mendonc et al., 2013) and ISIC (Codella et al.,
2017) datasets are presented in Figure 3.
From the ROC curve presented in Figure 3, we
show that the game theory holds the best result with
the value of AUC = 0.94 followed by the color
descriptor with the value of AUC = 0.90, then the
border with AUC = 0.83, asymmetry and diameter
with 0.75 and 0.74 respectively. These rates prove the
effectiveness of the proposed game theory modeling
as a combination scheme.
Figure 3: ROC Curves of ABCD features and the
proposed game theory modeling using PH2 dataset.
Figure 4: ROC Curves of ABCD features and the
proposed game theory modeling using ISIC dataset.
The graph of the Figure 4 represents the result
obtained from the evaluation of our approach on the
ISIC dataset (Codella et al., 2017); these curves were
developed from 1000 images from the ISIC dataset
(Codella et al., 2017). Our model of game theory has
the highest score with AUC = 0.93, the color
descriptor holds the second-best score with the AUC
value = 0.74, the asymmetry and the border parameter
come next with the area under the curve 0.67 and 0.60
respectively, the diameter descriptor is last with AUC
= 0.53. We find that the proposed approach has given
Melanoma Detection System based on a Game Theory Model
709
an excellent rating despite the fact that other
descriptors have not performed well, which proves the
performance of the proposed approach.
4.3 Comparison of the Game Theory
Modeling with Some Classifiers
In this section, the proposed classification scheme
based on zero-sum game theory modeling has been
confronted with four different classification systems
using the ABCD rule namely: Adaboost, KNN,
Bayes, and Random trees, testing on PH2 database
(Mendonc et al., 2013). The results of the classifiers
are provided from the works in (Pennisi et al., 2016)
adopting the implementation provided by Weka
(Witten et al., 2005). The ROC curves along with
the index AUC are used to illustrate this comparison.
The results are presented in figure 5.We remark that
the false-positive rate of our approach is minimal
compared to the other classifiers, so our game model
holds the maximum score with AUC = 0.94.
We can conclude that our method has proven
effective when compared with some interesting
classifiers. The proposed utility function allows to
our system to reduce significantly the false positive
rate (the benign skin lesion detected melanoma).
4.4 Comparison of the Proposed
Approach with State of Art
Methods
Finally, we present comparative results of the
proposed approach with recent state of art methods
tested on PH2 database. The comparison is
performed using three most used metrics: accuracy,
sensitivity, specificity. Table 1 summarizes the
obtained results.
Figure 5: Comparison of the proposed method to some
classifiers in PH2 dataset.
We can see that the results of our approach are better than
benchmarking results in terms of two metrics among the
three selected of the PH2 dataset. Furthermore our
algorithm is second ranked in sensitivity rate. The
benchmarking results are provided on the official website
(Mendonc et al., 2013) of the PH2 dataset. This confirms
that the performance of the proposed zero-sum game is
undeniable.
Table 1: Comparative results.
Methods Accurac
y
sensitivit
y
s
p
ecificit
y
Moradi and
Amiri 2019
93.50 100 91.81
Sadri et al.
2017
91.82 92.61 91
Gu et al.,2017 - 94,43 81.01
Bi et al 2016 92 87.5 93.13
Kruk et
al.2015
89.5 95 88.125
Our approach 94.5 95 94.375
5 CONCLUSION
We present in this paper a melanoma detection system
based on zero-sum game theory modeling. The proposed
system has ability to cope with subjective evaluation of
the different aspects of a skin lesion and to select the
appropriate characteristics for each suspect lesion. This
selection is performed using an interaction between
melanoma and non-melanoma agents where the set of
formulas involved in the computation of the features:
Asymmetry, Border, Color and diameter (ABCD) provide
the pure strategies of the game.
The utility function developed in our approach is able
to reduce significantly the false positive rate and to
maintain a good accuracy performance.
When tested on PH2 database (Mendonc et al., 2013),
the proposed algorithm was best ranked in terms of two
metrics among the three selected compared with five
recent states-of- art works
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