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

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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704

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



× 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=



4π 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:



log

(

)

log

(

)

(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).

(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



𝑁



(

𝑝



−𝑥

)







(7)

𝑝



is the i

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:





(8)







−



((



− m



)



(



)



)









((



−m



)



(



)



)

(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

VISAPP 2020 - 15th International Conference on Computer Vision Theory and Applications

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



)

where:



Melanoma palyer, non − Melanoma player



the set of players.



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





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

‖‖

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





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



)

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∈

ℝ





:𝑥



≥0 𝑒𝑡 𝑥











(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=𝐸𝑢

(

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 maximum “floor” of the Player 1

and minimum “ceiling” of player 2.

VISAPP 2020 - 15th International Conference on Computer Vision Theory and Applications

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

∗

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

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

sensitivit

ecificit

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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